Version abc61206

10 files changed, 3416 insertions, 0 deletions

diff --git a/src/opt/kit/kit.h b/src/opt/kit/kit.h
new file mode 100644
index 00000000..d97fca58
--- /dev/null
+++ b/src/opt/kit/kit.h
@@ -0,0 +1,334 @@
+/**CFile****************************************************************
+
+  FileName    [kit.h]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [External declarations.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kit.h,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#ifndef __KIT_H__
+#define __KIT_H__
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+////////////////////////////////////////////////////////////////////////
+///                          INCLUDES                                ///
+////////////////////////////////////////////////////////////////////////
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include <time.h>
+#include "vec.h"
+
+////////////////////////////////////////////////////////////////////////
+///                         PARAMETERS                               ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                         BASIC TYPES                              ///
+////////////////////////////////////////////////////////////////////////
+
+typedef struct Kit_Sop_t_ Kit_Sop_t;
+struct Kit_Sop_t_
+{
+    int               nCubes;         // the number of cubes
+    unsigned *        pCubes;         // the storage for cubes
+};
+
+typedef struct Kit_Edge_t_ Kit_Edge_t;
+struct Kit_Edge_t_
+{
+    unsigned          fCompl   :  1;   // the complemented bit
+    unsigned          Node     : 30;   // the decomposition node pointed by the edge
+};
+
+typedef struct Kit_Node_t_ Kit_Node_t;
+struct Kit_Node_t_
+{
+    Kit_Edge_t        eEdge0;          // the left child of the node
+    Kit_Edge_t        eEdge1;          // the right child of the node
+    // other info
+    void *            pFunc;           // the function of the node (BDD or AIG)
+    unsigned          Level    : 14;   // the level of this node in the global AIG
+    // printing info 
+    unsigned          fNodeOr  :  1;   // marks the original OR node
+    unsigned          fCompl0  :  1;   // marks the original complemented edge
+    unsigned          fCompl1  :  1;   // marks the original complemented edge
+    // latch info
+    unsigned          nLat0    :  5;   // the number of latches on the first edge
+    unsigned          nLat1    :  5;   // the number of latches on the second edge
+    unsigned          nLat2    :  5;   // the number of latches on the output edge
+};
+
+typedef struct Kit_Graph_t_ Kit_Graph_t;
+struct Kit_Graph_t_
+{
+    int               fConst;          // marks the constant 1 graph
+    int               nLeaves;         // the number of leaves
+    int               nSize;           // the number of nodes (including the leaves) 
+    int               nCap;            // the number of allocated nodes
+    Kit_Node_t *      pNodes;          // the array of leaves and internal nodes
+    Kit_Edge_t        eRoot;           // the pointer to the topmost node
+};
+
+////////////////////////////////////////////////////////////////////////
+///                      MACRO DEFINITIONS                           ///
+////////////////////////////////////////////////////////////////////////
+
+#ifndef ALLOC
+#define ALLOC(type, num)     ((type *) malloc(sizeof(type) * (num)))
+#endif
+
+#ifndef FREE
+#define FREE(obj)             ((obj) ? (free((char *) (obj)), (obj) = 0) : 0)
+#endif
+
+#ifndef REALLOC
+#define REALLOC(type, obj, num)    \
+        ((obj) ? ((type *) realloc((char *)(obj), sizeof(type) * (num))) : \
+         ((type *) malloc(sizeof(type) * (num))))
+#endif
+
+static inline int          Kit_CubeHasLit( unsigned uCube, int i )                        { return(uCube &  (unsigned)(1<<i)) > 0;  }
+static inline unsigned     Kit_CubeSetLit( unsigned uCube, int i )                        { return uCube |  (unsigned)(1<<i);       }
+static inline unsigned     Kit_CubeXorLit( unsigned uCube, int i )                        { return uCube ^  (unsigned)(1<<i);       }
+static inline unsigned     Kit_CubeRemLit( unsigned uCube, int i )                        { return uCube & ~(unsigned)(1<<i);       }
+
+static inline int          Kit_CubeContains( unsigned uLarge, unsigned uSmall )           { return (uLarge & uSmall) == uSmall;     }
+static inline unsigned     Kit_CubeSharp( unsigned uCube, unsigned uMask )                { return uCube & ~uMask;                  }
+static inline unsigned     Kit_CubeMask( int nVar )                                       { return (~(unsigned)0) >> (32-nVar);     }
+
+static inline int          Kit_CubeIsMarked( unsigned uCube )                             { return Kit_CubeHasLit( uCube, 31 );     }
+static inline unsigned     Kit_CubeMark( unsigned uCube )                                 { return Kit_CubeSetLit( uCube, 31 );     }
+static inline unsigned     Kit_CubeUnmark( unsigned uCube )                               { return Kit_CubeRemLit( uCube, 31 );     }
+
+static inline int          Kit_SopCubeNum( Kit_Sop_t * cSop )                             { return cSop->nCubes;                    }
+static inline unsigned     Kit_SopCube( Kit_Sop_t * cSop, int i )                         { return cSop->pCubes[i];                 }
+static inline void         Kit_SopShrink( Kit_Sop_t * cSop, int nCubesNew )               { cSop->nCubes = nCubesNew;               }
+static inline void         Kit_SopPushCube( Kit_Sop_t * cSop, unsigned uCube )            { cSop->pCubes[cSop->nCubes++] = uCube;   }
+static inline void         Kit_SopWriteCube( Kit_Sop_t * cSop, unsigned uCube, int i )    { cSop->pCubes[i] = uCube;                }
+
+static inline Kit_Edge_t   Kit_EdgeCreate( int Node, int fCompl )                         { Kit_Edge_t eEdge = { fCompl, Node }; return eEdge;  }
+static inline unsigned     Kit_EdgeToInt( Kit_Edge_t eEdge )                              { return (eEdge.Node << 1) | eEdge.fCompl;            }
+static inline Kit_Edge_t   Kit_IntToEdge( unsigned Edge )                                 { return Kit_EdgeCreate( Edge >> 1, Edge & 1 );       }
+static inline unsigned     Kit_EdgeToInt_( Kit_Edge_t eEdge )                             { return *(unsigned *)&eEdge;                         }
+static inline Kit_Edge_t   Kit_IntToEdge_( unsigned Edge )                                { return *(Kit_Edge_t *)&Edge;                        }
+
+static inline int          Kit_GraphIsConst( Kit_Graph_t * pGraph )                       { return pGraph->fConst;                              }
+static inline int          Kit_GraphIsConst0( Kit_Graph_t * pGraph )                      { return pGraph->fConst && pGraph->eRoot.fCompl;      }
+static inline int          Kit_GraphIsConst1( Kit_Graph_t * pGraph )                      { return pGraph->fConst && !pGraph->eRoot.fCompl;     }
+static inline int          Kit_GraphIsComplement( Kit_Graph_t * pGraph )                  { return pGraph->eRoot.fCompl;                        }
+static inline int          Kit_GraphIsVar( Kit_Graph_t * pGraph )                         { return pGraph->eRoot.Node < (unsigned)pGraph->nLeaves; }
+static inline void         Kit_GraphComplement( Kit_Graph_t * pGraph )                    { pGraph->eRoot.fCompl ^= 1;                          }
+static inline void         Kit_GraphSetRoot( Kit_Graph_t * pGraph, Kit_Edge_t eRoot )     { pGraph->eRoot = eRoot;                              }
+static inline int          Kit_GraphLeaveNum( Kit_Graph_t * pGraph )                      { return pGraph->nLeaves;                             }
+static inline int          Kit_GraphNodeNum( Kit_Graph_t * pGraph )                       { return pGraph->nSize - pGraph->nLeaves;             }
+static inline Kit_Node_t * Kit_GraphNode( Kit_Graph_t * pGraph, int i )                   { return pGraph->pNodes + i;                          }
+static inline Kit_Node_t * Kit_GraphNodeLast( Kit_Graph_t * pGraph )                      { return pGraph->pNodes + pGraph->nSize - 1;          }
+static inline int          Kit_GraphNodeInt( Kit_Graph_t * pGraph, Kit_Node_t * pNode )   { return pNode - pGraph->pNodes;                      }
+static inline int          Kit_GraphNodeIsVar( Kit_Graph_t * pGraph, Kit_Node_t * pNode ) { return Kit_GraphNodeInt(pGraph,pNode) < pGraph->nLeaves; }
+static inline Kit_Node_t * Kit_GraphVar( Kit_Graph_t * pGraph )                           { assert( Kit_GraphIsVar( pGraph ) );    return Kit_GraphNode( pGraph, pGraph->eRoot.Node ); }
+static inline int          Kit_GraphVarInt( Kit_Graph_t * pGraph )                        { assert( Kit_GraphIsVar( pGraph ) );    return Kit_GraphNodeInt( pGraph, Kit_GraphVar(pGraph) );}
+
+static inline int          Kit_Float2Int( float Val )     { return *((int *)&Val);               }
+static inline float        Kit_Int2Float( int Num )       { return *((float *)&Num);             }
+static inline int          Kit_BitWordNum( int nBits )    { return nBits/(8*sizeof(unsigned)) + ((nBits%(8*sizeof(unsigned))) > 0);  }
+static inline int          Kit_TruthWordNum( int nVars )  { return nVars <= 5 ? 1 : (1 << (nVars - 5)); }
+
+static inline void         Kit_TruthSetBit( unsigned * p, int Bit )   { p[Bit>>5] |= (1<<(Bit & 31));               }
+static inline void         Kit_TruthXorBit( unsigned * p, int Bit )   { p[Bit>>5] ^= (1<<(Bit & 31));               }
+static inline int          Kit_TruthHasBit( unsigned * p, int Bit )   { return (p[Bit>>5] & (1<<(Bit & 31))) > 0;   }
+
+static inline int Kit_WordCountOnes( unsigned uWord )
+{
+    uWord = (uWord & 0x55555555) + ((uWord>>1) & 0x55555555);
+    uWord = (uWord & 0x33333333) + ((uWord>>2) & 0x33333333);
+    uWord = (uWord & 0x0F0F0F0F) + ((uWord>>4) & 0x0F0F0F0F);
+    uWord = (uWord & 0x00FF00FF) + ((uWord>>8) & 0x00FF00FF);
+    return  (uWord & 0x0000FFFF) + (uWord>>16);
+}
+static inline int Kit_TruthCountOnes( unsigned * pIn, int nVars )
+{
+    int w, Counter = 0;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        Counter += Kit_WordCountOnes(pIn[w]);
+    return Counter;
+}
+static inline int Kit_TruthIsEqual( unsigned * pIn0, unsigned * pIn1, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        if ( pIn0[w] != pIn1[w] )
+            return 0;
+    return 1;
+}
+static inline int Kit_TruthIsConst0( unsigned * pIn, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        if ( pIn[w] )
+            return 0;
+    return 1;
+}
+static inline int Kit_TruthIsConst1( unsigned * pIn, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        if ( pIn[w] != ~(unsigned)0 )
+            return 0;
+    return 1;
+}
+static inline int Kit_TruthIsImply( unsigned * pIn1, unsigned * pIn2, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        if ( pIn1[w] & ~pIn2[w] )
+            return 0;
+    return 1;
+}
+static inline void Kit_TruthCopy( unsigned * pOut, unsigned * pIn, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = pIn[w];
+}
+static inline void Kit_TruthClear( unsigned * pOut, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = 0;
+}
+static inline void Kit_TruthFill( unsigned * pOut, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = ~(unsigned)0;
+}
+static inline void Kit_TruthNot( unsigned * pOut, unsigned * pIn, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = ~pIn[w];
+}
+static inline void Kit_TruthAnd( unsigned * pOut, unsigned * pIn0, unsigned * pIn1, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = pIn0[w] & pIn1[w];
+}
+static inline void Kit_TruthOr( unsigned * pOut, unsigned * pIn0, unsigned * pIn1, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = pIn0[w] | pIn1[w];
+}
+static inline void Kit_TruthSharp( unsigned * pOut, unsigned * pIn0, unsigned * pIn1, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = pIn0[w] & ~pIn1[w];
+}
+static inline void Kit_TruthNand( unsigned * pOut, unsigned * pIn0, unsigned * pIn1, int nVars )
+{
+    int w;
+    for ( w = Kit_TruthWordNum(nVars)-1; w >= 0; w-- )
+        pOut[w] = ~(pIn0[w] & pIn1[w]);
+}
+
+////////////////////////////////////////////////////////////////////////
+///                           ITERATORS                              ///
+////////////////////////////////////////////////////////////////////////
+
+#define Kit_SopForEachCube( cSop, uCube, i )                                      \
+    for ( i = 0; (i < Kit_SopCubeNum(cSop)) && ((uCube) = Kit_SopCube(cSop, i)); i++ )
+#define Kit_CubeForEachLiteral( uCube, Lit, nLits, i )                            \
+    for ( i = 0; (i < (nLits)) && ((Lit) = Kit_CubeHasLit(uCube, i)); i++ )
+
+#define Kit_GraphForEachLeaf( pGraph, pLeaf, i )                                              \
+    for ( i = 0; (i < (pGraph)->nLeaves) && (((pLeaf) = Kit_GraphNode(pGraph, i)), 1); i++ )
+#define Kit_GraphForEachNode( pGraph, pAnd, i )                                               \
+    for ( i = (pGraph)->nLeaves; (i < (pGraph)->nSize) && (((pAnd) = Kit_GraphNode(pGraph, i)), 1); i++ )
+
+////////////////////////////////////////////////////////////////////////
+///                    FUNCTION DECLARATIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/*=== kitBdd.c ==========================================================*/
+extern DdNode *        Kit_SopToBdd( DdManager * dd, Kit_Sop_t * cSop, int nVars );
+extern DdNode *        Kit_GraphToBdd( DdManager * dd, Kit_Graph_t * pGraph );
+extern DdNode *        Kit_TruthToBdd( DdManager * dd, unsigned * pTruth, int nVars );
+/*=== kitFactor.c ==========================================================*/
+extern Kit_Graph_t *   Kit_SopFactor( Vec_Int_t * vCover, int fCompl, int nVars, Vec_Int_t * vMemory );
+/*=== kitGraph.c ==========================================================*/
+extern Kit_Graph_t *   Kit_GraphCreate( int nLeaves );   
+extern Kit_Graph_t *   Kit_GraphCreateConst0();   
+extern Kit_Graph_t *   Kit_GraphCreateConst1();   
+extern Kit_Graph_t *   Kit_GraphCreateLeaf( int iLeaf, int nLeaves, int fCompl );   
+extern void            Kit_GraphFree( Kit_Graph_t * pGraph );   
+extern Kit_Node_t *    Kit_GraphAppendNode( Kit_Graph_t * pGraph );   
+extern Kit_Edge_t      Kit_GraphAddNodeAnd( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1 );
+extern Kit_Edge_t      Kit_GraphAddNodeOr( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1 );
+extern Kit_Edge_t      Kit_GraphAddNodeXor( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1, int Type );
+extern Kit_Edge_t      Kit_GraphAddNodeMux( Kit_Graph_t * pGraph, Kit_Edge_t eEdgeC, Kit_Edge_t eEdgeT, Kit_Edge_t eEdgeE, int Type );
+extern unsigned        Kit_GraphToTruth( Kit_Graph_t * pGraph );
+extern Kit_Graph_t *   Kit_TruthToGraph( unsigned * pTruth, int nVars, Vec_Int_t * vMemory );
+/*=== kitHop.c ==========================================================*/
+/*=== kitIsop.c ==========================================================*/
+extern int             Kit_TruthIsop( unsigned * puTruth, int nVars, Vec_Int_t * vMemory, int fTryBoth );
+/*=== kitSop.c ==========================================================*/
+extern void            Kit_SopCreate( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nVars, Vec_Int_t * vMemory );
+extern void            Kit_SopCreateInverse( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nVars, Vec_Int_t * vMemory );
+extern void            Kit_SopDup( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory );
+extern void            Kit_SopDivideByLiteralQuo( Kit_Sop_t * cSop, int iLit );
+extern void            Kit_SopDivideByCube( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory );
+extern void            Kit_SopDivideInternal( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory );
+extern void            Kit_SopMakeCubeFree( Kit_Sop_t * cSop );
+extern int             Kit_SopIsCubeFree( Kit_Sop_t * cSop );
+extern void            Kit_SopCommonCubeCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory );
+extern int             Kit_SopAnyLiteral( Kit_Sop_t * cSop, int nLits );
+extern int             Kit_SopDivisor( Kit_Sop_t * cResult, Kit_Sop_t * cSop, int nLits, Vec_Int_t * vMemory );
+extern void            Kit_SopBestLiteralCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, unsigned uCube, int nLits, Vec_Int_t * vMemory );
+/*=== kitTruth.c ==========================================================*/
+extern void            Kit_TruthSwapAdjacentVars( unsigned * pOut, unsigned * pIn, int nVars, int Start );
+extern void            Kit_TruthStretch( unsigned * pOut, unsigned * pIn, int nVars, int nVarsAll, unsigned Phase );
+extern void            Kit_TruthShrink( unsigned * pOut, unsigned * pIn, int nVars, int nVarsAll, unsigned Phase );
+extern int             Kit_TruthVarInSupport( unsigned * pTruth, int nVars, int iVar );
+extern int             Kit_TruthSupportSize( unsigned * pTruth, int nVars );
+extern int             Kit_TruthSupport( unsigned * pTruth, int nVars );
+extern void            Kit_TruthCofactor0( unsigned * pTruth, int nVars, int iVar );
+extern void            Kit_TruthCofactor1( unsigned * pTruth, int nVars, int iVar );
+extern void            Kit_TruthExist( unsigned * pTruth, int nVars, int iVar );
+extern void            Kit_TruthForall( unsigned * pTruth, int nVars, int iVar );
+extern void            Kit_TruthMux( unsigned * pOut, unsigned * pCof0, unsigned * pCof1, int nVars, int iVar );
+extern void            Kit_TruthChangePhase( unsigned * pTruth, int nVars, int iVar );
+extern int             Kit_TruthMinCofSuppOverlap( unsigned * pTruth, int nVars, int * pVarMin );
+extern void            Kit_TruthCountOnesInCofs( unsigned * pTruth, int nVars, short * pStore );
+extern unsigned        Kit_TruthHash( unsigned * pIn, int nWords );
+extern unsigned        Kit_TruthSemiCanonicize( unsigned * pInOut, unsigned * pAux, int nVars, char * pCanonPerm, short * pStore );
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
diff --git a/src/opt/kit/kitBdd.c b/src/opt/kit/kitBdd.c
new file mode 100644
index 00000000..ed978740
--- /dev/null
+++ b/src/opt/kit/kitBdd.c
@@ -0,0 +1,231 @@
+/**CFile****************************************************************
+
+  FileName    [kitBdd.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Procedures involving BDDs.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitBdd.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+#include "extra.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Derives the BDD for the given SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * Kit_SopToBdd( DdManager * dd, Kit_Sop_t * cSop, int nVars )
+{
+    DdNode * bSum, * bCube, * bTemp, * bVar;
+    unsigned uCube;
+    int Value, i, v;
+    assert( nVars < 16 );
+    // start the cover
+    bSum = Cudd_ReadLogicZero(dd);   Cudd_Ref( bSum );
+   // check the logic function of the node
+    Kit_SopForEachCube( cSop, uCube, i )
+    {
+        bCube = Cudd_ReadOne(dd);   Cudd_Ref( bCube );
+        for ( v = 0; v < nVars; v++ )
+        {
+            Value = ((uCube >> 2*v) & 3);
+            if ( Value == 1 )
+                bVar = Cudd_Not( Cudd_bddIthVar( dd, v ) );
+            else if ( Value == 2 )
+                bVar = Cudd_bddIthVar( dd, v );
+            else
+                continue;
+            bCube  = Cudd_bddAnd( dd, bTemp = bCube, bVar );   Cudd_Ref( bCube );
+            Cudd_RecursiveDeref( dd, bTemp );
+        }
+        bSum = Cudd_bddOr( dd, bTemp = bSum, bCube );   
+        Cudd_Ref( bSum );
+        Cudd_RecursiveDeref( dd, bTemp );
+        Cudd_RecursiveDeref( dd, bCube );
+    }
+    // complement the result if necessary
+    Cudd_Deref( bSum );
+    return bSum;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Converts graph to BDD.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * Kit_GraphToBdd( DdManager * dd, Kit_Graph_t * pGraph )
+{
+    DdNode * bFunc, * bFunc0, * bFunc1;
+    Kit_Node_t * pNode;
+    int i;
+
+    // sanity checks
+    assert( Kit_GraphLeaveNum(pGraph) >= 0 );
+    assert( Kit_GraphLeaveNum(pGraph) <= pGraph->nSize );
+
+    // check for constant function
+    if ( Kit_GraphIsConst(pGraph) )
+        return Cudd_NotCond( b1, Kit_GraphIsComplement(pGraph) );
+    // check for a literal
+    if ( Kit_GraphIsVar(pGraph) )
+        return Cudd_NotCond( Cudd_bddIthVar(dd, Kit_GraphVarInt(pGraph)), Kit_GraphIsComplement(pGraph) );
+
+    // assign the elementary variables
+    Kit_GraphForEachLeaf( pGraph, pNode, i )
+        pNode->pFunc = Cudd_bddIthVar( dd, i );
+
+    // compute the function for each internal node
+    Kit_GraphForEachNode( pGraph, pNode, i )
+    {
+        bFunc0 = Cudd_NotCond( Kit_GraphNode(pGraph, pNode->eEdge0.Node)->pFunc, pNode->eEdge0.fCompl ); 
+        bFunc1 = Cudd_NotCond( Kit_GraphNode(pGraph, pNode->eEdge1.Node)->pFunc, pNode->eEdge1.fCompl ); 
+        pNode->pFunc = Cudd_bddAnd( dd, bFunc0, bFunc1 );   Cudd_Ref( pNode->pFunc );
+    }
+
+    // deref the intermediate results
+    bFunc = pNode->pFunc;   Cudd_Ref( bFunc );
+    Kit_GraphForEachNode( pGraph, pNode, i )
+        Cudd_RecursiveDeref( dd, pNode->pFunc );
+    Cudd_Deref( bFunc );
+
+    // complement the result if necessary
+    return Cudd_NotCond( bFunc, Kit_GraphIsComplement(pGraph) );
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * Kit_TruthToBdd_rec( DdManager * dd, unsigned * pTruth, int iBit, int nVars, int nVarsTotal )
+{
+    DdNode * bF0, * bF1, * bF;
+    if ( nVars == 0 )
+    {
+        if ( pTruth[iBit>>5] & (1 << iBit&31) )
+            return b1;
+        return b0;
+    }
+    if ( nVars == 5 )
+    {
+        if ( pTruth[iBit>>5] == 0xFFFFFFFF )
+            return b1;
+        if ( pTruth[iBit>>5] == 0 )
+            return b0;
+    }
+    // other special cases can be added
+    bF0 = Kit_TruthToBdd_rec( dd, pTruth, iBit,                nVars-1, nVarsTotal );  Cudd_Ref( bF0 );
+    bF1 = Kit_TruthToBdd_rec( dd, pTruth, iBit+(1<<(nVars-1)), nVars-1, nVarsTotal );  Cudd_Ref( bF1 );
+    bF  = Cudd_bddIte( dd, dd->vars[nVarsTotal-nVars], bF1, bF0 );                     Cudd_Ref( bF );
+    Cudd_RecursiveDeref( dd, bF0 );
+    Cudd_RecursiveDeref( dd, bF1 );
+    Cudd_Deref( bF );
+    return bF;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Compute BDD corresponding to the truth table.]
+
+  Description [If truth table has N vars, the BDD depends on N topmost
+  variables of the BDD manager. The most significant variable of the table
+  is encoded by the topmost variable of the manager. BDD construction is 
+  efficient in this case because BDD is constructed one node at a time, 
+  by simply adding BDD nodes on top of existent BDD nodes.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+DdNode * Kit_TruthToBdd( DdManager * dd, unsigned * pTruth, int nVars )
+{
+    return Kit_TruthToBdd_rec( dd, pTruth, 0, nVars, nVars );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Verifies that the factoring is correct.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopFactorVerify( Vec_Int_t * vCover, Kit_Graph_t * pFForm, int nVars )
+{
+    static DdManager * dd = NULL;
+    Kit_Sop_t Sop, * cSop = &Sop;
+    DdNode * bFunc1, * bFunc2;
+    Vec_Int_t * vMemory;
+    int RetValue;
+    // get the manager
+    if ( dd == NULL )
+        dd = Cudd_Init( 16, 0, CUDD_UNIQUE_SLOTS, CUDD_CACHE_SLOTS, 0 );
+    // derive SOP
+    vMemory = Vec_IntAlloc( Vec_IntSize(vCover) );
+    Kit_SopCreate( cSop, vCover, nVars, vMemory );
+    // get the functions
+    bFunc1 = Kit_SopToBdd( dd, cSop, nVars );      Cudd_Ref( bFunc1 );
+    bFunc2 = Kit_GraphToBdd( dd, pFForm );         Cudd_Ref( bFunc2 );
+//Extra_bddPrint( dd, bFunc1 ); printf("\n");
+//Extra_bddPrint( dd, bFunc2 ); printf("\n");
+    RetValue = (bFunc1 == bFunc2);
+    if ( bFunc1 != bFunc2 )
+    {
+        int s;
+        Extra_bddPrint( dd, bFunc1 ); printf("\n");
+        Extra_bddPrint( dd, bFunc2 ); printf("\n");
+        s  = 0;
+    }
+    Cudd_RecursiveDeref( dd, bFunc1 );
+    Cudd_RecursiveDeref( dd, bFunc2 );
+    Vec_IntFree( vMemory );
+    return RetValue;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kitFactor.c b/src/opt/kit/kitFactor.c
new file mode 100644
index 00000000..618a4272
--- /dev/null
+++ b/src/opt/kit/kitFactor.c
@@ -0,0 +1,337 @@
+/**CFile****************************************************************
+
+  FileName    [kitFactor.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Algebraic factoring.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitFactor.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+// factoring fails if intermediate memory usage exceed this limit
+#define KIT_FACTOR_MEM_LIMIT  (1<<16)
+
+static Kit_Edge_t  Kit_SopFactor_rec( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, int nLits, Vec_Int_t * vMemory );
+static Kit_Edge_t  Kit_SopFactorLF_rec( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, Kit_Sop_t * cSimple, int nLits, Vec_Int_t * vMemory );
+static Kit_Edge_t  Kit_SopFactorTrivial( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, int nLits );
+static Kit_Edge_t  Kit_SopFactorTrivialCube( Kit_Graph_t * pFForm, unsigned uCube, int nLits );
+
+extern int         Kit_SopFactorVerify( Vec_Int_t * cSop, Kit_Graph_t * pFForm, int nVars );
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Factors the cover.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_SopFactor( Vec_Int_t * vCover, int fCompl, int nVars, Vec_Int_t * vMemory )
+{
+    Kit_Sop_t Sop, Res;
+    Kit_Sop_t * cSop = &Sop, * cRes = &Res;
+    Kit_Graph_t * pFForm;
+    Kit_Edge_t eRoot;
+    int nCubes = Vec_IntSize(vCover);
+
+    // works for up to 15 variables because divisin procedure
+    // used the last bit for marking the cubes going to the remainder
+    assert( nVars < 16 );
+
+    // check for trivial functions
+    if ( Vec_IntSize(vCover) == 0 )
+        return Kit_GraphCreateConst0();
+    if ( Vec_IntSize(vCover) == 1 && Vec_IntEntry(vCover, 0) == (int)Kit_CubeMask(nVars) )
+        return Kit_GraphCreateConst1();
+
+    // prepare memory manager
+//    Vec_IntClear( vMemory );
+    Vec_IntGrow( vMemory, KIT_FACTOR_MEM_LIMIT );
+
+    // perform CST
+    Kit_SopCreateInverse( cSop, vCover, 2 * nVars, vMemory ); // CST
+
+    // start the factored form
+    pFForm = Kit_GraphCreate( nVars );
+    // factor the cover
+    eRoot = Kit_SopFactor_rec( pFForm, cSop, 2 * nVars, vMemory );
+    // finalize the factored form
+    Kit_GraphSetRoot( pFForm, eRoot );
+    if ( fCompl )
+        Kit_GraphComplement( pFForm );
+
+    // verify the factored form
+//    Vec_IntShrink( vCover, nCubes );
+//    if ( !Kit_SopFactorVerify( vCover, pFForm, nVars ) )
+//        printf( "Verification has failed.\n" );
+    return pFForm;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Recursive factoring procedure.]
+
+  Description [For the pseudo-code, see Hachtel/Somenzi, 
+  Logic synthesis and verification algorithms, Kluwer, 1996, p. 432.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactor_rec( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, int nLits, Vec_Int_t * vMemory )
+{
+    Kit_Sop_t Div, Quo, Rem, Com;
+    Kit_Sop_t * cDiv = &Div, * cQuo = &Quo, * cRem = &Rem, * cCom = &Com;
+    Kit_Edge_t eNodeDiv, eNodeQuo, eNodeRem, eNodeAnd;
+
+    // make sure the cover contains some cubes
+    assert( Kit_SopCubeNum(cSop) > 0 );
+
+    // get the divisor
+    if ( !Kit_SopDivisor(cDiv, cSop, nLits, vMemory) )
+        return Kit_SopFactorTrivial( pFForm, cSop, nLits );
+
+    // divide the cover by the divisor
+    Kit_SopDivideInternal( cSop, cDiv, cQuo, cRem, vMemory );
+
+    // check the trivial case
+    assert( Kit_SopCubeNum(cQuo) > 0 );
+    if ( Kit_SopCubeNum(cQuo) == 1 )
+        return Kit_SopFactorLF_rec( pFForm, cSop, cQuo, nLits, vMemory );
+
+    // make the quotient cube free
+    Kit_SopMakeCubeFree( cQuo );
+
+    // divide the cover by the quotient
+    Kit_SopDivideInternal( cSop, cQuo, cDiv, cRem, vMemory );
+
+    // check the trivial case
+    if ( Kit_SopIsCubeFree( cDiv ) )
+    {
+        eNodeDiv = Kit_SopFactor_rec( pFForm, cDiv, nLits, vMemory );
+        eNodeQuo = Kit_SopFactor_rec( pFForm, cQuo, nLits, vMemory );
+        eNodeAnd = Kit_GraphAddNodeAnd( pFForm, eNodeDiv, eNodeQuo );
+        if ( Kit_SopCubeNum(cRem) == 0 )
+            return eNodeAnd;
+        eNodeRem = Kit_SopFactor_rec( pFForm, cRem, nLits, vMemory );
+        return Kit_GraphAddNodeOr( pFForm, eNodeAnd, eNodeRem );
+    }
+
+    // get the common cube
+    Kit_SopCommonCubeCover( cCom, cDiv, vMemory );
+
+    // solve the simple problem
+    return Kit_SopFactorLF_rec( pFForm, cSop, cCom, nLits, vMemory );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Internal recursive factoring procedure for the leaf case.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactorLF_rec( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, Kit_Sop_t * cSimple, int nLits, Vec_Int_t * vMemory )
+{
+    Kit_Sop_t Div, Quo, Rem;
+    Kit_Sop_t * cDiv = &Div, * cQuo = &Quo, * cRem = &Rem;
+    Kit_Edge_t eNodeDiv, eNodeQuo, eNodeRem, eNodeAnd;
+    assert( Kit_SopCubeNum(cSimple) == 1 );
+    // get the most often occurring literal
+    Kit_SopBestLiteralCover( cDiv, cSop, Kit_SopCube(cSimple, 0), nLits, vMemory );
+    // divide the cover by the literal
+    Kit_SopDivideByCube( cSop, cDiv, cQuo, cRem, vMemory );
+    // get the node pointer for the literal
+    eNodeDiv = Kit_SopFactorTrivialCube( pFForm, Kit_SopCube(cDiv, 0), nLits );
+    // factor the quotient and remainder
+    eNodeQuo = Kit_SopFactor_rec( pFForm, cQuo, nLits, vMemory );
+    eNodeAnd = Kit_GraphAddNodeAnd( pFForm, eNodeDiv, eNodeQuo );
+    if ( Kit_SopCubeNum(cRem) == 0 )
+        return eNodeAnd;
+    eNodeRem = Kit_SopFactor_rec( pFForm, cRem, nLits, vMemory );
+    return Kit_GraphAddNodeOr( pFForm, eNodeAnd, eNodeRem );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Factoring cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactorTrivialCube_rec( Kit_Graph_t * pFForm, unsigned uCube, int nStart, int nFinish )
+{
+    Kit_Edge_t eNode1, eNode2;
+    int i, iLit, nLits, nLits1, nLits2;
+    // count the number of literals in this interval
+    nLits = 0;
+    for ( i = nStart; i < nFinish; i++ )
+        if ( Kit_CubeHasLit(uCube, i) )
+        {
+            iLit = i;
+            nLits++;
+        }
+    // quit if there is only one literal        
+    if ( nLits == 1 )
+        return Kit_EdgeCreate( iLit/2, iLit%2 ); // CST
+    // split the literals into two parts
+    nLits1 = nLits/2;
+    nLits2 = nLits - nLits1;
+//    nLits2 = nLits/2;
+//    nLits1 = nLits - nLits2;
+    // find the splitting point
+    nLits = 0;
+    for ( i = nStart; i < nFinish; i++ )
+        if ( Kit_CubeHasLit(uCube, i) )
+        {
+            if ( nLits == nLits1 )
+                break;
+            nLits++;
+        }
+    // recursively construct the tree for the parts
+    eNode1 = Kit_SopFactorTrivialCube_rec( pFForm, uCube, nStart, i  );
+    eNode2 = Kit_SopFactorTrivialCube_rec( pFForm, uCube, i, nFinish );
+    return Kit_GraphAddNodeAnd( pFForm, eNode1, eNode2 );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Factoring cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactorTrivialCube( Kit_Graph_t * pFForm, unsigned uCube, int nLits )
+{
+    return Kit_SopFactorTrivialCube_rec( pFForm, uCube, 0, nLits );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Factoring SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactorTrivial_rec( Kit_Graph_t * pFForm, unsigned * pCubes, int nCubes, int nLits )
+{
+    Kit_Edge_t eNode1, eNode2;
+    int nCubes1, nCubes2;
+    if ( nCubes == 1 )
+        return Kit_SopFactorTrivialCube_rec( pFForm, pCubes[0], 0, nLits );
+    // split the cubes into two parts
+    nCubes1 = nCubes/2;
+    nCubes2 = nCubes - nCubes1;
+//    nCubes2 = nCubes/2;
+//    nCubes1 = nCubes - nCubes2;
+    // recursively construct the tree for the parts
+    eNode1 = Kit_SopFactorTrivial_rec( pFForm, pCubes,           nCubes1, nLits );
+    eNode2 = Kit_SopFactorTrivial_rec( pFForm, pCubes + nCubes1, nCubes2, nLits );
+    return Kit_GraphAddNodeOr( pFForm, eNode1, eNode2 );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Factoring the cover, which has no algebraic divisors.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_SopFactorTrivial( Kit_Graph_t * pFForm, Kit_Sop_t * cSop, int nLits )
+{
+    return Kit_SopFactorTrivial_rec( pFForm, cSop->pCubes, cSop->nCubes, nLits );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Testing procedure for the factoring code.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_FactorTest( unsigned * pTruth, int nVars )
+{
+    Vec_Int_t * vCover, * vMemory;
+    Kit_Graph_t * pGraph;
+//    unsigned uTruthRes;
+    int RetValue;
+
+    // derive SOP
+    vCover = Vec_IntAlloc( 0 );
+    RetValue = Kit_TruthIsop( pTruth, nVars, vCover, 0 );
+    assert( RetValue == 0 );
+
+    // derive factored form
+    vMemory = Vec_IntAlloc( 0 );
+    pGraph = Kit_SopFactor( vCover, 0, nVars, vMemory );
+/*
+    // derive truth table
+    assert( nVars <= 5 );
+    uTruthRes = Kit_GraphToTruth( pGraph );
+    if ( uTruthRes != pTruth[0] )
+        printf( "Verification failed!" );
+*/
+    printf( "Vars = %2d. Cubes = %3d. FFNodes = %3d. FF_memory = %3d.\n",
+        nVars, Vec_IntSize(vCover), Kit_GraphNodeNum(pGraph), Vec_IntSize(vMemory) );
+
+    Vec_IntFree( vMemory );
+    Vec_IntFree( vCover );
+    Kit_GraphFree( pGraph );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kitGraph.c b/src/opt/kit/kitGraph.c
new file mode 100644
index 00000000..e2172ca3
--- /dev/null
+++ b/src/opt/kit/kitGraph.c
@@ -0,0 +1,367 @@
+/**CFile****************************************************************
+
+  FileName    [kitGraph.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Decomposition graph representation.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitGraph.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Creates a graph with the given number of leaves.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_GraphCreate( int nLeaves )   
+{
+    Kit_Graph_t * pGraph;
+    pGraph = ALLOC( Kit_Graph_t, 1 );
+    memset( pGraph, 0, sizeof(Kit_Graph_t) );
+    pGraph->nLeaves = nLeaves;
+    pGraph->nSize = nLeaves;
+    pGraph->nCap = 2 * nLeaves + 50;
+    pGraph->pNodes = ALLOC( Kit_Node_t, pGraph->nCap );
+    memset( pGraph->pNodes, 0, sizeof(Kit_Node_t) * pGraph->nSize );
+    return pGraph;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates constant 0 graph.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_GraphCreateConst0()   
+{
+    Kit_Graph_t * pGraph;
+    pGraph = ALLOC( Kit_Graph_t, 1 );
+    memset( pGraph, 0, sizeof(Kit_Graph_t) );
+    pGraph->fConst = 1;
+    pGraph->eRoot.fCompl = 1;
+    return pGraph;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates constant 1 graph.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_GraphCreateConst1()   
+{
+    Kit_Graph_t * pGraph;
+    pGraph = ALLOC( Kit_Graph_t, 1 );
+    memset( pGraph, 0, sizeof(Kit_Graph_t) );
+    pGraph->fConst = 1;
+    return pGraph;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates the literal graph.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_GraphCreateLeaf( int iLeaf, int nLeaves, int fCompl )   
+{
+    Kit_Graph_t * pGraph;
+    assert( 0 <= iLeaf && iLeaf < nLeaves );
+    pGraph = Kit_GraphCreate( nLeaves );
+    pGraph->eRoot.Node   = iLeaf;
+    pGraph->eRoot.fCompl = fCompl;
+    return pGraph;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates a graph with the given number of leaves.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_GraphFree( Kit_Graph_t * pGraph )   
+{
+    FREE( pGraph->pNodes );
+    free( pGraph );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Appends a new node to the graph.]
+
+  Description [This procedure is meant for internal use.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Node_t * Kit_GraphAppendNode( Kit_Graph_t * pGraph )   
+{
+    Kit_Node_t * pNode;
+    if ( pGraph->nSize == pGraph->nCap )
+    {
+        pGraph->pNodes = REALLOC( Kit_Node_t, pGraph->pNodes, 2 * pGraph->nCap ); 
+        pGraph->nCap   = 2 * pGraph->nCap;
+    }
+    pNode = pGraph->pNodes + pGraph->nSize++;
+    memset( pNode, 0, sizeof(Kit_Node_t) );
+    return pNode;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates an AND node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_GraphAddNodeAnd( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1 )
+{
+    Kit_Node_t * pNode;
+    // get the new node
+    pNode = Kit_GraphAppendNode( pGraph );
+    // set the inputs and other info
+    pNode->eEdge0 = eEdge0;
+    pNode->eEdge1 = eEdge1;
+    pNode->fCompl0 = eEdge0.fCompl;
+    pNode->fCompl1 = eEdge1.fCompl;
+    return Kit_EdgeCreate( pGraph->nSize - 1, 0 );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates an OR node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_GraphAddNodeOr( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1 )
+{
+    Kit_Node_t * pNode;
+    // get the new node
+    pNode = Kit_GraphAppendNode( pGraph );
+    // set the inputs and other info
+    pNode->eEdge0 = eEdge0;
+    pNode->eEdge1 = eEdge1;
+    pNode->fCompl0 = eEdge0.fCompl;
+    pNode->fCompl1 = eEdge1.fCompl;
+    // make adjustments for the OR gate
+    pNode->fNodeOr = 1;
+    pNode->eEdge0.fCompl = !pNode->eEdge0.fCompl;
+    pNode->eEdge1.fCompl = !pNode->eEdge1.fCompl;
+    return Kit_EdgeCreate( pGraph->nSize - 1, 1 );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates an XOR node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_GraphAddNodeXor( Kit_Graph_t * pGraph, Kit_Edge_t eEdge0, Kit_Edge_t eEdge1, int Type )
+{
+    Kit_Edge_t eNode0, eNode1, eNode;
+    if ( Type == 0 )
+    {
+        // derive the first AND
+        eEdge0.fCompl ^= 1;
+        eNode0 = Kit_GraphAddNodeAnd( pGraph, eEdge0, eEdge1 );
+        eEdge0.fCompl ^= 1;
+        // derive the second AND
+        eEdge1.fCompl ^= 1;
+        eNode1 = Kit_GraphAddNodeAnd( pGraph, eEdge0, eEdge1 );
+        // derive the final OR
+        eNode = Kit_GraphAddNodeOr( pGraph, eNode0, eNode1 );
+    }
+    else
+    {
+        // derive the first AND
+        eNode0 = Kit_GraphAddNodeAnd( pGraph, eEdge0, eEdge1 );
+        // derive the second AND
+        eEdge0.fCompl ^= 1;
+        eEdge1.fCompl ^= 1;
+        eNode1 = Kit_GraphAddNodeAnd( pGraph, eEdge0, eEdge1 );
+        // derive the final OR
+        eNode = Kit_GraphAddNodeOr( pGraph, eNode0, eNode1 );
+        eNode.fCompl ^= 1;
+    }
+    return eNode;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates an XOR node.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Edge_t Kit_GraphAddNodeMux( Kit_Graph_t * pGraph, Kit_Edge_t eEdgeC, Kit_Edge_t eEdgeT, Kit_Edge_t eEdgeE, int Type )
+{
+    Kit_Edge_t eNode0, eNode1, eNode;
+    if ( Type == 0 )
+    {
+        // derive the first AND
+        eNode0 = Kit_GraphAddNodeAnd( pGraph, eEdgeC, eEdgeT );
+        // derive the second AND
+        eEdgeC.fCompl ^= 1;
+        eNode1 = Kit_GraphAddNodeAnd( pGraph, eEdgeC, eEdgeE );
+        // derive the final OR
+        eNode = Kit_GraphAddNodeOr( pGraph, eNode0, eNode1 );
+    }
+    else
+    {
+        // complement the arguments
+        eEdgeT.fCompl ^= 1;
+        eEdgeE.fCompl ^= 1;
+        // derive the first AND
+        eNode0 = Kit_GraphAddNodeAnd( pGraph, eEdgeC, eEdgeT );
+        // derive the second AND
+        eEdgeC.fCompl ^= 1;
+        eNode1 = Kit_GraphAddNodeAnd( pGraph, eEdgeC, eEdgeE );
+        // derive the final OR
+        eNode = Kit_GraphAddNodeOr( pGraph, eNode0, eNode1 );
+        eNode.fCompl ^= 1;
+    }
+    return eNode;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derives the truth table.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned Kit_GraphToTruth( Kit_Graph_t * pGraph )
+{
+    unsigned uTruths[5] = { 0xAAAAAAAA, 0xCCCCCCCC, 0xF0F0F0F0, 0xFF00FF00, 0xFFFF0000 };
+    unsigned uTruth, uTruth0, uTruth1;
+    Kit_Node_t * pNode;
+    int i;
+
+    // sanity checks
+    assert( Kit_GraphLeaveNum(pGraph) >= 0 );
+    assert( Kit_GraphLeaveNum(pGraph) <= pGraph->nSize );
+    assert( Kit_GraphLeaveNum(pGraph) <= 5 );
+
+    // check for constant function
+    if ( Kit_GraphIsConst(pGraph) )
+        return Kit_GraphIsComplement(pGraph)? 0 : ~((unsigned)0);
+    // check for a literal
+    if ( Kit_GraphIsVar(pGraph) )
+        return Kit_GraphIsComplement(pGraph)? ~uTruths[Kit_GraphVarInt(pGraph)] : uTruths[Kit_GraphVarInt(pGraph)];
+
+    // assign the elementary variables
+    Kit_GraphForEachLeaf( pGraph, pNode, i )
+        pNode->pFunc = (void *)uTruths[i];
+
+    // compute the function for each internal node
+    Kit_GraphForEachNode( pGraph, pNode, i )
+    {
+        uTruth0 = (unsigned)Kit_GraphNode(pGraph, pNode->eEdge0.Node)->pFunc;
+        uTruth1 = (unsigned)Kit_GraphNode(pGraph, pNode->eEdge1.Node)->pFunc;
+        uTruth0 = pNode->eEdge0.fCompl? ~uTruth0 : uTruth0;
+        uTruth1 = pNode->eEdge1.fCompl? ~uTruth1 : uTruth1;
+        uTruth = uTruth0 & uTruth1;
+        pNode->pFunc = (void *)uTruth;
+    }
+
+    // complement the result if necessary
+    return Kit_GraphIsComplement(pGraph)? ~uTruth : uTruth;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derives the factored form from the truth table.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Kit_Graph_t * Kit_TruthToGraph( unsigned * pTruth, int nVars, Vec_Int_t * vMemory )
+{
+    Kit_Graph_t * pGraph;
+    int RetValue;
+    // derive SOP
+    RetValue = Kit_TruthIsop( pTruth, nVars, vMemory, 0 );
+    assert( RetValue == 0 );
+    // derive factored form
+    pGraph = Kit_SopFactor( vMemory, 0, nVars, vMemory );
+    return pGraph;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
diff --git a/src/opt/kit/kitHop.c b/src/opt/kit/kitHop.c
new file mode 100644
index 00000000..95461c4e
--- /dev/null
+++ b/src/opt/kit/kitHop.c
@@ -0,0 +1,115 @@
+/**CFile****************************************************************
+
+  FileName    [kitHop.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Procedures involving AIGs.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitHop.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+#include "hop.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+
+/**Function*************************************************************
+
+  Synopsis    [Transforms the decomposition graph into the AIG.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Hop_Obj_t * Kit_GraphToHopInternal( Hop_Man_t * pMan, Kit_Graph_t * pGraph )
+{
+    Kit_Node_t * pNode;
+    Hop_Obj_t * pAnd0, * pAnd1;
+    int i;
+    // check for constant function
+    if ( Kit_GraphIsConst(pGraph) )
+        return Hop_NotCond( Hop_ManConst1(pMan), Kit_GraphIsComplement(pGraph) );
+    // check for a literal
+    if ( Kit_GraphIsVar(pGraph) )
+        return Hop_NotCond( Kit_GraphVar(pGraph)->pFunc, Kit_GraphIsComplement(pGraph) );
+    // build the AIG nodes corresponding to the AND gates of the graph
+    Kit_GraphForEachNode( pGraph, pNode, i )
+    {
+        pAnd0 = Hop_NotCond( Kit_GraphNode(pGraph, pNode->eEdge0.Node)->pFunc, pNode->eEdge0.fCompl ); 
+        pAnd1 = Hop_NotCond( Kit_GraphNode(pGraph, pNode->eEdge1.Node)->pFunc, pNode->eEdge1.fCompl ); 
+        pNode->pFunc = Hop_And( pMan, pAnd0, pAnd1 );
+    }
+    // complement the result if necessary
+    return Hop_NotCond( pNode->pFunc, Kit_GraphIsComplement(pGraph) );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Strashes one logic node using its SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Hop_Obj_t * Kit_GraphToHop( Hop_Man_t * pMan, Kit_Graph_t * pGraph )
+{
+    Kit_Node_t * pNode;
+    int i;
+    // collect the fanins
+    Kit_GraphForEachLeaf( pGraph, pNode, i )
+        pNode->pFunc = Hop_IthVar( pMan, i );
+    // perform strashing
+    return Kit_GraphToHopInternal( pMan, pGraph );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Strashes one logic node using its SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Hop_Obj_t * Kit_CoverToHop( Hop_Man_t * pMan, Vec_Int_t * vCover, int nVars, Vec_Int_t * vMemory )
+{
+    Kit_Graph_t * pGraph;
+    Hop_Obj_t * pFunc;
+    // perform factoring
+    pGraph = Kit_SopFactor( vCover, 0, nVars, vMemory );
+    // convert graph to the AIG
+    pFunc = Kit_GraphToHop( pMan, pGraph );
+    Kit_GraphFree( pGraph );
+    return pFunc;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kitIsop.c b/src/opt/kit/kitIsop.c
new file mode 100644
index 00000000..420cb16f
--- /dev/null
+++ b/src/opt/kit/kitIsop.c
@@ -0,0 +1,319 @@
+/**CFile****************************************************************
+
+  FileName    [kitIsop.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [ISOP computation based on Morreale's algorithm.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitIsop.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+// ISOP computation fails if intermediate memory usage exceed this limit
+#define KIT_ISOP_MEM_LIMIT  (1<<16)
+
+// static procedures to compute ISOP
+static unsigned * Kit_TruthIsop_rec( unsigned * puOn, unsigned * puOnDc, int nVars, Kit_Sop_t * pcRes, Vec_Int_t * vStore );
+static unsigned   Kit_TruthIsop5_rec( unsigned uOn, unsigned uOnDc, int nVars, Kit_Sop_t * pcRes, Vec_Int_t * vStore );
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Computes ISOP from TT.]
+
+  Description [Returns the cover in vMemory. Uses the rest of array in vMemory
+  as an intermediate memory storage. Returns the cover with -1 cubes, if the
+  the computation exceeded the memory limit (KIT_ISOP_MEM_LIMIT words of
+  intermediate data).]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthIsop( unsigned * puTruth, int nVars, Vec_Int_t * vMemory, int fTryBoth )
+{
+    Kit_Sop_t cRes, * pcRes = &cRes;
+    Kit_Sop_t cRes2, * pcRes2 = &cRes2;
+    unsigned * pResult;
+    int RetValue = 0;
+    assert( nVars >= 0 && nVars < 16 );
+    // if nVars < 5, make sure it does not depend on those vars
+//    for ( i = nVars; i < 5; i++ )
+//        assert( !Extra_TruthVarInSupport(puTruth, 5, i) );
+    // prepare memory manager
+    Vec_IntClear( vMemory );
+    Vec_IntGrow( vMemory, KIT_ISOP_MEM_LIMIT );
+    // compute ISOP for the direct polarity
+    pResult = Kit_TruthIsop_rec( puTruth, puTruth, nVars, pcRes, vMemory );
+    if ( pcRes->nCubes == -1 )
+    {
+        vMemory->nSize = -1;
+        return 0;
+    }
+    assert( Extra_TruthIsEqual( puTruth, pResult, nVars ) );
+    if ( fTryBoth )
+    {
+        // compute ISOP for the complemented polarity
+        Extra_TruthNot( puTruth, puTruth, nVars );
+        pResult = Kit_TruthIsop_rec( puTruth, puTruth, nVars, pcRes2, vMemory );
+        if ( pcRes2->nCubes >= 0 )
+        {
+            assert( Extra_TruthIsEqual( puTruth, pResult, nVars ) );
+            if ( pcRes->nCubes > pcRes2->nCubes )
+            {
+                RetValue = 1;
+                pcRes = pcRes2;
+            }
+        }
+        Extra_TruthNot( puTruth, puTruth, nVars );
+    }
+//    printf( "%d ", vMemory->nSize );
+    // move the cover representation to the beginning of the memory buffer
+    memmove( vMemory->pArray, pcRes->pCubes, pcRes->nCubes * sizeof(unsigned) );
+    Vec_IntShrink( vMemory, pcRes->nCubes );
+    return RetValue;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes ISOP 6 variables or more.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned * Kit_TruthIsop_rec( unsigned * puOn, unsigned * puOnDc, int nVars, Kit_Sop_t * pcRes, Vec_Int_t * vStore )
+{
+    Kit_Sop_t cRes0, cRes1, cRes2;
+    Kit_Sop_t * pcRes0 = &cRes0, * pcRes1 = &cRes1, * pcRes2 = &cRes2;
+    unsigned * puRes0, * puRes1, * puRes2;
+    unsigned * puOn0, * puOn1, * puOnDc0, * puOnDc1, * pTemp, * pTemp0, * pTemp1;
+    int i, k, Var, nWords, nWordsAll;
+//    assert( Extra_TruthIsImply( puOn, puOnDc, nVars ) );
+    // allocate room for the resulting truth table
+    nWordsAll = Extra_TruthWordNum( nVars );
+    pTemp = Vec_IntFetch( vStore, nWordsAll );
+    if ( pTemp == NULL )
+    {
+        pcRes->nCubes = -1;
+        return NULL;
+    }
+    // check for constants
+    if ( Extra_TruthIsConst0( puOn, nVars ) )
+    {
+        pcRes->nCubes = 0;
+        pcRes->pCubes = NULL;
+        Extra_TruthClear( pTemp, nVars );
+        return pTemp;
+    }
+    if ( Extra_TruthIsConst1( puOnDc, nVars ) )
+    {
+        pcRes->nCubes = 1;
+        pcRes->pCubes = Vec_IntFetch( vStore, 1 );
+        if ( pcRes->pCubes == NULL )
+        {
+            pcRes->nCubes = -1;
+            return NULL;
+        }
+        pcRes->pCubes[0] = 0;
+        Extra_TruthFill( pTemp, nVars );
+        return pTemp;
+    }
+    assert( nVars > 0 );
+    // find the topmost var
+    for ( Var = nVars-1; Var >= 0; Var-- )
+        if ( Extra_TruthVarInSupport( puOn, nVars, Var ) || 
+             Extra_TruthVarInSupport( puOnDc, nVars, Var ) )
+             break;
+    assert( Var >= 0 );
+    // consider a simple case when one-word computation can be used
+    if ( Var < 5 )
+    {
+        unsigned uRes = Kit_TruthIsop5_rec( puOn[0], puOnDc[0], Var+1, pcRes, vStore );
+        for ( i = 0; i < nWordsAll; i++ )
+            pTemp[i] = uRes;
+        return pTemp;
+    }
+    assert( Var >= 5 );
+    nWords = Extra_TruthWordNum( Var );
+    // cofactor
+    puOn0   = puOn;    puOn1   = puOn + nWords;
+    puOnDc0 = puOnDc;  puOnDc1 = puOnDc + nWords;
+    pTemp0  = pTemp;   pTemp1  = pTemp + nWords;
+    // solve for cofactors
+    Extra_TruthSharp( pTemp0, puOn0, puOnDc1, Var );
+    puRes0 = Kit_TruthIsop_rec( pTemp0, puOnDc0, Var, pcRes0, vStore );
+    if ( pcRes0->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return NULL;
+    }
+    Extra_TruthSharp( pTemp1, puOn1, puOnDc0, Var );
+    puRes1 = Kit_TruthIsop_rec( pTemp1, puOnDc1, Var, pcRes1, vStore );
+    if ( pcRes1->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return NULL;
+    }
+    Extra_TruthSharp( pTemp0, puOn0, puRes0, Var );
+    Extra_TruthSharp( pTemp1, puOn1, puRes1, Var );
+    Extra_TruthOr( pTemp0, pTemp0, pTemp1, Var );
+    Extra_TruthAnd( pTemp1, puOnDc0, puOnDc1, Var );
+    puRes2 = Kit_TruthIsop_rec( pTemp0, pTemp1, Var, pcRes2, vStore );
+    if ( pcRes2->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return NULL;
+    }
+    // create the resulting cover
+    pcRes->nCubes = pcRes0->nCubes + pcRes1->nCubes + pcRes2->nCubes;
+    pcRes->pCubes = Vec_IntFetch( vStore, pcRes->nCubes );
+    if ( pcRes->pCubes == NULL )
+    {
+        pcRes->nCubes = -1;
+        return NULL;
+    }
+    k = 0;
+    for ( i = 0; i < pcRes0->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes0->pCubes[i] | (1 << ((Var<<1)+0));
+    for ( i = 0; i < pcRes1->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes1->pCubes[i] | (1 << ((Var<<1)+1));
+    for ( i = 0; i < pcRes2->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes2->pCubes[i];
+    assert( k == pcRes->nCubes );
+    // create the resulting truth table
+    Extra_TruthOr( pTemp0, puRes0, puRes2, Var );
+    Extra_TruthOr( pTemp1, puRes1, puRes2, Var );
+    // copy the table if needed
+    nWords <<= 1;
+    for ( i = 1; i < nWordsAll/nWords; i++ )
+        for ( k = 0; k < nWords; k++ )
+            pTemp[i*nWords + k] = pTemp[k];
+    // verify in the end
+//    assert( Extra_TruthIsImply( puOn, pTemp, nVars ) );
+//    assert( Extra_TruthIsImply( pTemp, puOnDc, nVars ) );
+    return pTemp;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes ISOP for 5 variables or less.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned Kit_TruthIsop5_rec( unsigned uOn, unsigned uOnDc, int nVars, Kit_Sop_t * pcRes, Vec_Int_t * vStore )
+{
+    unsigned uMasks[5] = { 0xAAAAAAAA, 0xCCCCCCCC, 0xF0F0F0F0, 0xFF00FF00, 0xFFFF0000 };
+    Kit_Sop_t cRes0, cRes1, cRes2;
+    Kit_Sop_t * pcRes0 = &cRes0, * pcRes1 = &cRes1, * pcRes2 = &cRes2;
+    unsigned uOn0, uOn1, uOnDc0, uOnDc1, uRes0, uRes1, uRes2;
+    int i, k, Var;
+    assert( nVars <= 5 );
+    assert( (uOn & ~uOnDc) == 0 );
+    if ( uOn == 0 )
+    {
+        pcRes->nCubes = 0;
+        pcRes->pCubes = NULL;
+        return 0;
+    }
+    if ( uOnDc == 0xFFFFFFFF )
+    {
+        pcRes->nCubes = 1;
+        pcRes->pCubes = Vec_IntFetch( vStore, 1 );
+        if ( pcRes->pCubes == NULL )
+        {
+            pcRes->nCubes = -1;
+            return 0;
+        }
+        pcRes->pCubes[0] = 0;
+        return 0xFFFFFFFF;
+    }
+    assert( nVars > 0 );
+    // find the topmost var
+    for ( Var = nVars-1; Var >= 0; Var-- )
+        if ( Extra_TruthVarInSupport( &uOn, 5, Var ) || 
+             Extra_TruthVarInSupport( &uOnDc, 5, Var ) )
+             break;
+    assert( Var >= 0 );
+    // cofactor
+    uOn0   = uOn1   = uOn;
+    uOnDc0 = uOnDc1 = uOnDc;
+    Extra_TruthCofactor0( &uOn0, Var + 1, Var );
+    Extra_TruthCofactor1( &uOn1, Var + 1, Var );
+    Extra_TruthCofactor0( &uOnDc0, Var + 1, Var );
+    Extra_TruthCofactor1( &uOnDc1, Var + 1, Var );
+    // solve for cofactors
+    uRes0 = Kit_TruthIsop5_rec( uOn0 & ~uOnDc1, uOnDc0, Var, pcRes0, vStore );
+    if ( pcRes0->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return 0;
+    }
+    uRes1 = Kit_TruthIsop5_rec( uOn1 & ~uOnDc0, uOnDc1, Var, pcRes1, vStore );
+    if ( pcRes1->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return 0;
+    }
+    uRes2 = Kit_TruthIsop5_rec( (uOn0 & ~uRes0) | (uOn1 & ~uRes1), uOnDc0 & uOnDc1, Var, pcRes2, vStore );
+    if ( pcRes2->nCubes == -1 )
+    {
+        pcRes->nCubes = -1;
+        return 0;
+    }
+    // create the resulting cover
+    pcRes->nCubes = pcRes0->nCubes + pcRes1->nCubes + pcRes2->nCubes;
+    pcRes->pCubes = Vec_IntFetch( vStore, pcRes->nCubes );
+    if ( pcRes->pCubes == NULL )
+    {
+        pcRes->nCubes = -1;
+        return 0;
+    }
+    k = 0;
+    for ( i = 0; i < pcRes0->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes0->pCubes[i] | (1 << ((Var<<1)+0));
+    for ( i = 0; i < pcRes1->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes1->pCubes[i] | (1 << ((Var<<1)+1));
+    for ( i = 0; i < pcRes2->nCubes; i++ )
+        pcRes->pCubes[k++] = pcRes2->pCubes[i];
+    assert( k == pcRes->nCubes );
+    // derive the final truth table
+    uRes2 |= (uRes0 & ~uMasks[Var]) | (uRes1 & uMasks[Var]);
+//    assert( (uOn & ~uRes2) == 0 );
+//    assert( (uRes2 & ~uOnDc) == 0 );
+    return uRes2;
+}
+
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kitSop.c b/src/opt/kit/kitSop.c
new file mode 100644
index 00000000..3fa81351
--- /dev/null
+++ b/src/opt/kit/kitSop.c
@@ -0,0 +1,570 @@
+/**CFile****************************************************************
+
+  FileName    [kitSop.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Procedures involving SOPs.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitSop.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Creates SOP from the cube array.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopCreate( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nVars, Vec_Int_t * vMemory )
+{
+    unsigned uCube;
+    int i;
+    // start the cover
+    cResult->nCubes = 0;
+    cResult->pCubes = Vec_IntFetch( vMemory, Vec_IntSize(vInput) );
+    // add the cubes
+    Vec_IntForEachEntry( vInput, uCube, i )
+        Kit_SopPushCube( cResult, uCube );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates SOP from the cube array.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopCreateInverse( Kit_Sop_t * cResult, Vec_Int_t * vInput, int nLits, Vec_Int_t * vMemory )
+{
+    unsigned uCube, uMask = 0;
+    int i, nCubes = Vec_IntSize(vInput);
+    // start the cover
+    cResult->nCubes = 0;
+    cResult->pCubes = Vec_IntFetch( vMemory, nCubes );
+    // add the cubes
+//    Vec_IntForEachEntry( vInput, uCube, i )
+    for ( i = 0; i < nCubes; i++ )
+    {
+        uCube = Vec_IntEntry( vInput, i );
+        uMask = ((uCube | (uCube >> 1)) & 0x55555555);
+        uMask |= (uMask << 1);
+        Kit_SopPushCube( cResult, uCube ^ uMask );
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Duplicates SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopDup( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory )
+{
+    unsigned uCube;
+    int i;
+    // start the cover
+    cResult->nCubes = 0;
+    cResult->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
+    // add the cubes
+    Kit_SopForEachCube( cSop, uCube, i )
+        Kit_SopPushCube( cResult, uCube );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derives the quotient of division by literal.]
+
+  Description [Reduces the cover to be equal to the result of
+  division of the given cover by the literal.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopDivideByLiteralQuo( Kit_Sop_t * cSop, int iLit )
+{
+    unsigned uCube;
+    int i, k = 0;
+    Kit_SopForEachCube( cSop, uCube, i )
+    {
+        if ( Kit_CubeHasLit(uCube, iLit) )
+            Kit_SopWriteCube( cSop, Kit_CubeRemLit(uCube, iLit), k++ );
+    }
+    Kit_SopShrink( cSop, k );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Divides cover by one cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopDivideByCube( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory )
+{
+    unsigned uCube, uDiv;
+    int i;
+    // get the only cube
+    assert( Kit_SopCubeNum(cDiv) == 1 );
+    uDiv = Kit_SopCube(cDiv, 0);
+    // allocate covers
+    vQuo->nCubes = 0;
+    vQuo->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
+    vRem->nCubes = 0;
+    vRem->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) );
+    // sort the cubes
+    Kit_SopForEachCube( cSop, uCube, i )
+    {
+        if ( Kit_CubeContains( uCube, uDiv ) )
+            Kit_SopPushCube( vQuo, Kit_CubeSharp(uCube, uDiv) );
+        else
+            Kit_SopPushCube( vRem, uCube );
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Divides cover by one cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopDivideInternal( Kit_Sop_t * cSop, Kit_Sop_t * cDiv, Kit_Sop_t * vQuo, Kit_Sop_t * vRem, Vec_Int_t * vMemory )
+{
+    unsigned uCube, uDiv, uCube2, uDiv2, uQuo;
+    int i, i2, k, k2, nCubesRem;
+    assert( Kit_SopCubeNum(cSop) >= Kit_SopCubeNum(cDiv) );
+    // consider special case
+    if ( Kit_SopCubeNum(cDiv) == 1 )
+    {
+        Kit_SopDivideByCube( cSop, cDiv, vQuo, vRem, vMemory );
+        return;
+    }
+    // allocate quotient
+    vQuo->nCubes = 0;
+    vQuo->pCubes = Vec_IntFetch( vMemory, Kit_SopCubeNum(cSop) / Kit_SopCubeNum(cDiv) );
+    // for each cube of the cover
+    // it either belongs to the quotient or to the remainder
+    Kit_SopForEachCube( cSop, uCube, i )
+    {
+        // skip taken cubes
+        if ( Kit_CubeIsMarked(uCube) )
+            continue;
+        // find a matching cube in the divisor
+        Kit_SopForEachCube( cDiv, uDiv, k )
+            if ( Kit_CubeContains( uCube, uDiv ) )
+                break;
+        // the cube is not found 
+        if ( k == Kit_SopCubeNum(cDiv) )
+            continue;
+        // the quotient cube exists
+        uQuo = Kit_CubeSharp( uCube, uDiv );
+        // find corresponding cubes for other cubes of the divisor
+        Kit_SopForEachCube( cDiv, uDiv2, k2 )
+        {
+            if ( k2 == k )
+                continue;
+            // find a matching cube
+            Kit_SopForEachCube( cSop, uCube2, i2 )
+            {
+                // skip taken cubes
+                if ( Kit_CubeIsMarked(uCube2) )
+                    continue;
+                // check if the cube can be used
+                if ( Kit_CubeContains( uCube2, uDiv2 ) && uQuo == Kit_CubeSharp( uCube2, uDiv2 ) )
+                    break;
+            }
+            // the case when the cube is not found
+            if ( i2 == Kit_SopCubeNum(cSop) )
+                break;
+        }
+        // we did not find some cubes - continue looking at other cubes
+        if ( k2 != Kit_SopCubeNum(cDiv) )
+            continue;
+        // we found all cubes - add the quotient cube
+        Kit_SopPushCube( vQuo, uQuo );
+
+        // mark the first cube
+        Kit_SopWriteCube( cSop, Kit_CubeMark(uCube), i );
+        // mark other cubes that have this quotient
+        Kit_SopForEachCube( cDiv, uDiv2, k2 )
+        {
+            if ( k2 == k )
+                continue;
+            // find a matching cube
+            Kit_SopForEachCube( cSop, uCube2, i2 )
+            {
+                // skip taken cubes
+                if ( Kit_CubeIsMarked(uCube2) )
+                    continue;
+                // check if the cube can be used
+                if ( Kit_CubeContains( uCube2, uDiv2 ) && uQuo == Kit_CubeSharp( uCube2, uDiv2 ) )
+                    break;
+            }
+            assert( i2 < Kit_SopCubeNum(cSop) );
+            // the cube is found, mark it 
+            // (later we will add all unmarked cubes to the remainder)
+            Kit_SopWriteCube( cSop, Kit_CubeMark(uCube2), i2 );
+        }
+    }
+    // determine the number of cubes in the remainder
+    nCubesRem = Kit_SopCubeNum(cSop) - Kit_SopCubeNum(vQuo) * Kit_SopCubeNum(cDiv);
+    // allocate remainder
+    vRem->nCubes = 0;
+    vRem->pCubes = Vec_IntFetch( vMemory, nCubesRem );
+    // finally add the remaining unmarked cubes to the remainder 
+    // and clean the marked cubes in the cover
+    Kit_SopForEachCube( cSop, uCube, i )
+    {
+        if ( !Kit_CubeIsMarked(uCube) )
+        {
+            Kit_SopPushCube( vRem, uCube );
+            continue;
+        }
+        Kit_SopWriteCube( cSop, Kit_CubeUnmark(uCube), i );
+    }
+    assert( nCubesRem == Kit_SopCubeNum(vRem) );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Returns the common cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline unsigned Kit_SopCommonCube( Kit_Sop_t * cSop )
+{
+    unsigned uMask, uCube;
+    int i;
+    uMask = ~(unsigned)0;
+    Kit_SopForEachCube( cSop, uCube, i )
+        uMask &= uCube;
+    return uMask;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Makes the cover cube-free.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopMakeCubeFree( Kit_Sop_t * cSop )
+{
+    unsigned uMask, uCube;
+    int i;
+    uMask = Kit_SopCommonCube( cSop );
+    if ( uMask == 0 )
+        return;
+    // remove the common cube
+    Kit_SopForEachCube( cSop, uCube, i )
+        Kit_SopWriteCube( cSop, Kit_CubeSharp(uCube, uMask), i );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks if the cover is cube-free.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopIsCubeFree( Kit_Sop_t * cSop )
+{
+    return Kit_SopCommonCube( cSop ) == 0;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Creates SOP composes of the common cube of the given SOP.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopCommonCubeCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, Vec_Int_t * vMemory )
+{
+    assert( Kit_SopCubeNum(cSop) > 0 );
+    cResult->nCubes = 0;
+    cResult->pCubes = Vec_IntFetch( vMemory, 1 );
+    Kit_SopPushCube( cResult, Kit_SopCommonCube(cSop) );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Find any literal that occurs more than once.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopAnyLiteral( Kit_Sop_t * cSop, int nLits )
+{
+    unsigned uCube;
+    int i, k, nLitsCur;
+    // go through each literal
+    for ( i = 0; i < nLits; i++ )
+    {
+        // go through all the cubes
+        nLitsCur = 0;
+        Kit_SopForEachCube( cSop, uCube, k )
+            if ( Kit_CubeHasLit(uCube, i) )
+                nLitsCur++;
+        if ( nLitsCur > 1 )
+            return i;
+    }
+    return -1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Find the least often occurring literal.]
+
+  Description [Find the least often occurring literal among those
+  that occur more than once.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopWorstLiteral( Kit_Sop_t * cSop, int nLits )
+{
+    unsigned uCube;
+    int i, k, iMin, nLitsMin, nLitsCur;
+    int fUseFirst = 1;
+
+    // go through each literal
+    iMin = -1;
+    nLitsMin = 1000000;
+    for ( i = 0; i < nLits; i++ )
+    {
+        // go through all the cubes
+        nLitsCur = 0;
+        Kit_SopForEachCube( cSop, uCube, k )
+            if ( Kit_CubeHasLit(uCube, i) )
+                nLitsCur++;
+        // skip the literal that does not occur or occurs once
+        if ( nLitsCur < 2 )
+            continue;
+        // check if this is the best literal
+        if ( fUseFirst )
+        {
+            if ( nLitsMin > nLitsCur )
+            {
+                nLitsMin = nLitsCur;
+                iMin = i;
+            }
+        }
+        else
+        {
+            if ( nLitsMin >= nLitsCur )
+            {
+                nLitsMin = nLitsCur;
+                iMin = i;
+            }
+        }
+    }
+    if ( nLitsMin < 1000000 )
+        return iMin;
+    return -1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Find the least often occurring literal.]
+
+  Description [Find the least often occurring literal among those
+  that occur more than once.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopBestLiteral( Kit_Sop_t * cSop, int nLits, unsigned uMask )
+{
+    unsigned uCube;
+    int i, k, iMax, nLitsMax, nLitsCur;
+    int fUseFirst = 1;
+
+    // go through each literal
+    iMax = -1;
+    nLitsMax = -1;
+    for ( i = 0; i < nLits; i++ )
+    {
+        if ( !Kit_CubeHasLit(uMask, i) )
+            continue;
+        // go through all the cubes
+        nLitsCur = 0;
+        Kit_SopForEachCube( cSop, uCube, k )
+            if ( Kit_CubeHasLit(uCube, i) )
+                nLitsCur++;
+        // skip the literal that does not occur or occurs once
+        if ( nLitsCur < 2 )
+            continue;
+        // check if this is the best literal
+        if ( fUseFirst )
+        {
+            if ( nLitsMax < nLitsCur )
+            {
+                nLitsMax = nLitsCur;
+                iMax = i;
+            }
+        }
+        else
+        {
+            if ( nLitsMax <= nLitsCur )
+            {
+                nLitsMax = nLitsCur;
+                iMax = i;
+            }
+        }
+    }
+    if ( nLitsMax >= 0 )
+        return iMax;
+    return -1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes a level-zero kernel.]
+
+  Description [Modifies the cover to contain one level-zero kernel.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopDivisorZeroKernel_rec( Kit_Sop_t * cSop, int nLits )
+{
+    int iLit;
+    // find any literal that occurs at least two times
+    iLit = Kit_SopWorstLiteral( cSop, nLits );
+    if ( iLit == -1 )
+        return;
+    // derive the cube-free quotient
+    Kit_SopDivideByLiteralQuo( cSop, iLit ); // the same cover
+    Kit_SopMakeCubeFree( cSop );             // the same cover
+    // call recursively
+    Kit_SopDivisorZeroKernel_rec( cSop, nLits );    // the same cover
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes the quick divisor of the cover.]
+
+  Description [Returns 0, if there is no divisor other than trivial.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_SopDivisor( Kit_Sop_t * cResult, Kit_Sop_t * cSop, int nLits, Vec_Int_t * vMemory )
+{
+    if ( Kit_SopCubeNum(cSop) <= 1 )
+        return 0;
+    if ( Kit_SopAnyLiteral( cSop, nLits ) == -1 )
+        return 0;
+    // duplicate the cover
+    Kit_SopDup( cResult, cSop, vMemory );
+    // perform the kerneling
+    Kit_SopDivisorZeroKernel_rec( cResult, nLits );
+    assert( Kit_SopCubeNum(cResult) > 0 );
+    return 1;
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Create the one-literal cover with the best literal from cSop.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_SopBestLiteralCover( Kit_Sop_t * cResult, Kit_Sop_t * cSop, unsigned uCube, int nLits, Vec_Int_t * vMemory )
+{
+    int iLitBest;
+    // get the best literal
+    iLitBest = Kit_SopBestLiteral( cSop, nLits, uCube );
+    // start the cover
+    cResult->nCubes = 0;
+    cResult->pCubes = Vec_IntFetch( vMemory, 1 );
+    // set the cube
+    Kit_SopPushCube( cResult, Kit_CubeSetLit(0, iLitBest) );
+}
+
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kitTruth.c b/src/opt/kit/kitTruth.c
new file mode 100644
index 00000000..5df10d63
--- /dev/null
+++ b/src/opt/kit/kitTruth.c
@@ -0,0 +1,1088 @@
+/**CFile****************************************************************
+
+  FileName    [kitTruth.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    [Procedures involving truth tables.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kitTruth.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+static unsigned s_VarMasks[5][2] = {
+    { 0x33333333, 0xAAAAAAAA },
+    { 0x55555555, 0xCCCCCCCC },
+    { 0x0F0F0F0F, 0xF0F0F0F0 },
+    { 0x00FF00FF, 0xFF00FF00 },
+    { 0x0000FFFF, 0xFFFF0000 }
+};
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    [Swaps two adjacent variables in the truth table.]
+
+  Description [Swaps var number Start and var number Start+1 (0-based numbers).
+  The input truth table is pIn. The output truth table is pOut.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthSwapAdjacentVars( unsigned * pOut, unsigned * pIn, int nVars, int iVar )
+{
+    static unsigned PMasks[4][3] = {
+        { 0x99999999, 0x22222222, 0x44444444 },
+        { 0xC3C3C3C3, 0x0C0C0C0C, 0x30303030 },
+        { 0xF00FF00F, 0x00F000F0, 0x0F000F00 },
+        { 0xFF0000FF, 0x0000FF00, 0x00FF0000 }
+    };
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step, Shift;
+
+    assert( iVar < nVars - 1 );
+    if ( iVar < 4 )
+    {
+        Shift = (1 << iVar);
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pIn[i] & PMasks[iVar][0]) | ((pIn[i] & PMasks[iVar][1]) << Shift) | ((pIn[i] & PMasks[iVar][2]) >> Shift);
+    }
+    else if ( iVar > 4 )
+    {
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 4*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+                pOut[i] = pIn[i];
+            for ( i = 0; i < Step; i++ )
+                pOut[Step+i] = pIn[2*Step+i];
+            for ( i = 0; i < Step; i++ )
+                pOut[2*Step+i] = pIn[Step+i];
+            for ( i = 0; i < Step; i++ )
+                pOut[3*Step+i] = pIn[3*Step+i];
+            pIn  += 4*Step;
+            pOut += 4*Step;
+        }
+    }
+    else // if ( iVar == 4 )
+    {
+        for ( i = 0; i < nWords; i += 2 )
+        {
+            pOut[i]   = (pIn[i]   & 0x0000FFFF) | ((pIn[i+1] & 0x0000FFFF) << 16);
+            pOut[i+1] = (pIn[i+1] & 0xFFFF0000) | ((pIn[i]   & 0xFFFF0000) >> 16);
+        }
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Swaps two adjacent variables in the truth table.]
+
+  Description [Swaps var number Start and var number Start+1 (0-based numbers).
+  The input truth table is pIn. The output truth table is pOut.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthSwapAdjacentVars2( unsigned * pIn, unsigned * pOut, int nVars, int Start )
+{
+    int nWords = (nVars <= 5)? 1 : (1 << (nVars-5));
+    int i, k, Step;
+
+    assert( Start < nVars - 1 );
+    switch ( Start )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pIn[i] & 0x99999999) | ((pIn[i] & 0x22222222) << 1) | ((pIn[i] & 0x44444444) >> 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pIn[i] & 0xC3C3C3C3) | ((pIn[i] & 0x0C0C0C0C) << 2) | ((pIn[i] & 0x30303030) >> 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pIn[i] & 0xF00FF00F) | ((pIn[i] & 0x00F000F0) << 4) | ((pIn[i] & 0x0F000F00) >> 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pIn[i] & 0xFF0000FF) | ((pIn[i] & 0x0000FF00) << 8) | ((pIn[i] & 0x00FF0000) >> 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i += 2 )
+        {
+            pOut[i]   = (pIn[i]   & 0x0000FFFF) | ((pIn[i+1] & 0x0000FFFF) << 16);
+            pOut[i+1] = (pIn[i+1] & 0xFFFF0000) | ((pIn[i]   & 0xFFFF0000) >> 16);
+        }
+        return;
+    default:
+        Step = (1 << (Start - 5));
+        for ( k = 0; k < nWords; k += 4*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+                pOut[i] = pIn[i];
+            for ( i = 0; i < Step; i++ )
+                pOut[Step+i] = pIn[2*Step+i];
+            for ( i = 0; i < Step; i++ )
+                pOut[2*Step+i] = pIn[Step+i];
+            for ( i = 0; i < Step; i++ )
+                pOut[3*Step+i] = pIn[3*Step+i];
+            pIn  += 4*Step;
+            pOut += 4*Step;
+        }
+        return;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Expands the truth table according to the phase.]
+
+  Description [The input and output truth tables are in pIn/pOut. The current number
+  of variables is nVars. The total number of variables in nVarsAll. The last argument
+  (Phase) contains shows where the variables should go.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthStretch( unsigned * pOut, unsigned * pIn, int nVars, int nVarsAll, unsigned Phase )
+{
+    unsigned * pTemp;
+    int i, k, Var = nVars - 1, Counter = 0;
+    for ( i = nVarsAll - 1; i >= 0; i-- )
+        if ( Phase & (1 << i) )
+        {
+            for ( k = Var; k < i; k++ )
+            {
+                Kit_TruthSwapAdjacentVars( pOut, pIn, nVarsAll, k );
+                pTemp = pIn; pIn = pOut; pOut = pTemp;
+                Counter++;
+            }
+            Var--;
+        }
+    assert( Var == -1 );
+    // swap if it was moved an even number of times
+    if ( !(Counter & 1) )
+        Kit_TruthCopy( pOut, pIn, nVarsAll );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Shrinks the truth table according to the phase.]
+
+  Description [The input and output truth tables are in pIn/pOut. The current number
+  of variables is nVars. The total number of variables in nVarsAll. The last argument
+  (Phase) contains shows what variables should remain.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthShrink( unsigned * pOut, unsigned * pIn, int nVars, int nVarsAll, unsigned Phase )
+{
+    unsigned * pTemp;
+    int i, k, Var = 0, Counter = 0;
+    for ( i = 0; i < nVarsAll; i++ )
+        if ( Phase & (1 << i) )
+        {
+            for ( k = i-1; k >= Var; k-- )
+            {
+                Kit_TruthSwapAdjacentVars( pOut, pIn, nVarsAll, k );
+                pTemp = pIn; pIn = pOut; pOut = pTemp;
+                Counter++;
+            }
+            Var++;
+        }
+    assert( Var == nVars );
+    // swap if it was moved an even number of times
+    if ( !(Counter & 1) )
+        Kit_TruthCopy( pOut, pIn, nVarsAll );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Returns 1 if TT depends on the given variable.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthVarInSupport( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            if ( (pTruth[i] & 0x55555555) != ((pTruth[i] & 0xAAAAAAAA) >> 1) )
+                return 1;
+        return 0;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            if ( (pTruth[i] & 0x33333333) != ((pTruth[i] & 0xCCCCCCCC) >> 2) )
+                return 1;
+        return 0;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            if ( (pTruth[i] & 0x0F0F0F0F) != ((pTruth[i] & 0xF0F0F0F0) >> 4) )
+                return 1;
+        return 0;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            if ( (pTruth[i] & 0x00FF00FF) != ((pTruth[i] & 0xFF00FF00) >> 8) )
+                return 1;
+        return 0;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            if ( (pTruth[i] & 0x0000FFFF) != ((pTruth[i] & 0xFFFF0000) >> 16) )
+                return 1;
+        return 0;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+                if ( pTruth[i] != pTruth[Step+i] )
+                    return 1;
+            pTruth += 2*Step;
+        }
+        return 0;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Returns the number of support vars.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthSupportSize( unsigned * pTruth, int nVars )
+{
+    int i, Counter = 0;
+    for ( i = 0; i < nVars; i++ )
+        Counter += Kit_TruthVarInSupport( pTruth, nVars, i );
+    return Counter;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Returns support of the function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthSupport( unsigned * pTruth, int nVars )
+{
+    int i, Support = 0;
+    for ( i = 0; i < nVars; i++ )
+        if ( Kit_TruthVarInSupport( pTruth, nVars, i ) )
+            Support |= (1 << i);
+    return Support;
+}
+
+
+
+/**Function*************************************************************
+
+  Synopsis    [Computes positive cofactor of the function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthCofactor1( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0xAAAAAAAA) | ((pTruth[i] & 0xAAAAAAAA) >> 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0xCCCCCCCC) | ((pTruth[i] & 0xCCCCCCCC) >> 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0xF0F0F0F0) | ((pTruth[i] & 0xF0F0F0F0) >> 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0xFF00FF00) | ((pTruth[i] & 0xFF00FF00) >> 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0xFFFF0000) | ((pTruth[i] & 0xFFFF0000) >> 16);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+                pTruth[i] = pTruth[Step+i];
+            pTruth += 2*Step;
+        }
+        return;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes negative cofactor of the function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthCofactor0( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0x55555555) | ((pTruth[i] & 0x55555555) << 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0x33333333) | ((pTruth[i] & 0x33333333) << 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0x0F0F0F0F) | ((pTruth[i] & 0x0F0F0F0F) << 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0x00FF00FF) | ((pTruth[i] & 0x00FF00FF) << 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = (pTruth[i] & 0x0000FFFF) | ((pTruth[i] & 0x0000FFFF) << 16);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+                pTruth[Step+i] = pTruth[i];
+            pTruth += 2*Step;
+        }
+        return;
+    }
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Existentially quantifies the variable.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthExist( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] |=  ((pTruth[i] & 0xAAAAAAAA) >> 1) | ((pTruth[i] & 0x55555555) << 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] |=  ((pTruth[i] & 0xCCCCCCCC) >> 2) | ((pTruth[i] & 0x33333333) << 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] |=  ((pTruth[i] & 0xF0F0F0F0) >> 4) | ((pTruth[i] & 0x0F0F0F0F) << 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] |=  ((pTruth[i] & 0xFF00FF00) >> 8) | ((pTruth[i] & 0x00FF00FF) << 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] |=  ((pTruth[i] & 0xFFFF0000) >> 16) | ((pTruth[i] & 0x0000FFFF) << 16);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+            {
+                pTruth[i]     |= pTruth[Step+i];
+                pTruth[Step+i] = pTruth[i];
+            }
+            pTruth += 2*Step;
+        }
+        return;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Existentially quantifies the variable.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthForall( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] &=  ((pTruth[i] & 0xAAAAAAAA) >> 1) | ((pTruth[i] & 0x55555555) << 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] &=  ((pTruth[i] & 0xCCCCCCCC) >> 2) | ((pTruth[i] & 0x33333333) << 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] &=  ((pTruth[i] & 0xF0F0F0F0) >> 4) | ((pTruth[i] & 0x0F0F0F0F) << 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] &=  ((pTruth[i] & 0xFF00FF00) >> 8) | ((pTruth[i] & 0x00FF00FF) << 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] &=  ((pTruth[i] & 0xFFFF0000) >> 16) | ((pTruth[i] & 0x0000FFFF) << 16);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+            {
+                pTruth[i]     &= pTruth[Step+i];
+                pTruth[Step+i] = pTruth[i];
+            }
+            pTruth += 2*Step;
+        }
+        return;
+    }
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Computes negative cofactor of the function.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthMux( unsigned * pOut, unsigned * pCof0, unsigned * pCof1, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pCof0[i] & 0x55555555) | (pCof1[i] & 0xAAAAAAAA);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pCof0[i] & 0x33333333) | (pCof1[i] & 0xCCCCCCCC);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pCof0[i] & 0x0F0F0F0F) | (pCof1[i] & 0xF0F0F0F0);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pCof0[i] & 0x00FF00FF) | (pCof1[i] & 0xFF00FF00);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pOut[i] = (pCof0[i] & 0x0000FFFF) | (pCof1[i] & 0xFFFF0000);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+            {
+                pOut[i]      = pCof0[i];
+                pOut[Step+i] = pCof1[Step+i];
+            }
+            pOut += 2*Step;
+        }
+        return;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks symmetry of two variables.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthVarsSymm( unsigned * pTruth, int nVars, int iVar0, int iVar1 )
+{
+    static unsigned uTemp0[16], uTemp1[16];
+    assert( nVars <= 9 );
+    // compute Cof01
+    Kit_TruthCopy( uTemp0, pTruth, nVars );
+    Kit_TruthCofactor0( uTemp0, nVars, iVar0 );
+    Kit_TruthCofactor1( uTemp0, nVars, iVar1 );
+    // compute Cof10
+    Kit_TruthCopy( uTemp1, pTruth, nVars );
+    Kit_TruthCofactor1( uTemp1, nVars, iVar0 );
+    Kit_TruthCofactor0( uTemp1, nVars, iVar1 );
+    // compare
+    return Kit_TruthIsEqual( uTemp0, uTemp1, nVars );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Checks antisymmetry of two variables.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthVarsAntiSymm( unsigned * pTruth, int nVars, int iVar0, int iVar1 )
+{
+    static unsigned uTemp0[16], uTemp1[16];
+    assert( nVars <= 9 );
+    // compute Cof00
+    Kit_TruthCopy( uTemp0, pTruth, nVars );
+    Kit_TruthCofactor0( uTemp0, nVars, iVar0 );
+    Kit_TruthCofactor0( uTemp0, nVars, iVar1 );
+    // compute Cof11
+    Kit_TruthCopy( uTemp1, pTruth, nVars );
+    Kit_TruthCofactor1( uTemp1, nVars, iVar0 );
+    Kit_TruthCofactor1( uTemp1, nVars, iVar1 );
+    // compare
+    return Kit_TruthIsEqual( uTemp0, uTemp1, nVars );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Changes phase of the function w.r.t. one variable.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthChangePhase( unsigned * pTruth, int nVars, int iVar )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Step;
+    unsigned Temp;
+
+    assert( iVar < nVars );
+    switch ( iVar )
+    {
+    case 0:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = ((pTruth[i] & 0x55555555) << 1) | ((pTruth[i] & 0xAAAAAAAA) >> 1);
+        return;
+    case 1:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = ((pTruth[i] & 0x33333333) << 2) | ((pTruth[i] & 0xCCCCCCCC) >> 2);
+        return;
+    case 2:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = ((pTruth[i] & 0x0F0F0F0F) << 4) | ((pTruth[i] & 0xF0F0F0F0) >> 4);
+        return;
+    case 3:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = ((pTruth[i] & 0x00FF00FF) << 8) | ((pTruth[i] & 0xFF00FF00) >> 8);
+        return;
+    case 4:
+        for ( i = 0; i < nWords; i++ )
+            pTruth[i] = ((pTruth[i] & 0x0000FFFF) << 16) | ((pTruth[i] & 0xFFFF0000) >> 16);
+        return;
+    default:
+        Step = (1 << (iVar - 5));
+        for ( k = 0; k < nWords; k += 2*Step )
+        {
+            for ( i = 0; i < Step; i++ )
+            {
+                Temp = pTruth[i];
+                pTruth[i] = pTruth[Step+i];
+                pTruth[Step+i] = Temp;
+            }
+            pTruth += 2*Step;
+        }
+        return;
+    }
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Computes minimum overlap in supports of cofactors.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Kit_TruthMinCofSuppOverlap( unsigned * pTruth, int nVars, int * pVarMin )
+{
+    static unsigned uCofactor[16];
+    int i, ValueCur, ValueMin, VarMin;
+    unsigned uSupp0, uSupp1;
+    int nVars0, nVars1;
+    assert( nVars <= 9 );
+    ValueMin = 32;
+    VarMin   = -1;
+    for ( i = 0; i < nVars; i++ )
+    {
+        // get negative cofactor
+        Kit_TruthCopy( uCofactor, pTruth, nVars );
+        Kit_TruthCofactor0( uCofactor, nVars, i );
+        uSupp0 = Kit_TruthSupport( uCofactor, nVars );
+        nVars0 = Kit_WordCountOnes( uSupp0 );
+//Kit_PrintBinary( stdout, &uSupp0, 8 ); printf( "\n" );
+        // get positive cofactor
+        Kit_TruthCopy( uCofactor, pTruth, nVars );
+        Kit_TruthCofactor1( uCofactor, nVars, i );
+        uSupp1 = Kit_TruthSupport( uCofactor, nVars );
+        nVars1 = Kit_WordCountOnes( uSupp1 );
+//Kit_PrintBinary( stdout, &uSupp1, 8 ); printf( "\n" );
+        // get the number of common vars
+        ValueCur = Kit_WordCountOnes( uSupp0 & uSupp1 );
+        if ( ValueMin > ValueCur && nVars0 <= 5 && nVars1 <= 5 )
+        {
+            ValueMin = ValueCur;
+            VarMin = i;
+        }
+        if ( ValueMin == 0 )
+            break;
+    }
+    if ( pVarMin )
+        *pVarMin = VarMin;
+    return ValueMin;
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Counts the number of 1's in each cofactor.]
+
+  Description [The resulting numbers are stored in the array of shorts, 
+  whose length is 2*nVars. The number of 1's is counted in a different
+  space than the original function. For example, if the function depends 
+  on k variables, the cofactors are assumed to depend on k-1 variables.]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Kit_TruthCountOnesInCofs( unsigned * pTruth, int nVars, short * pStore )
+{
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, k, Counter;
+    memset( pStore, 0, sizeof(short) * 2 * nVars );
+    if ( nVars <= 5 )
+    {
+        if ( nVars > 0 )
+        {
+            pStore[2*0+0] = Kit_WordCountOnes( pTruth[0] & 0x55555555 );
+            pStore[2*0+1] = Kit_WordCountOnes( pTruth[0] & 0xAAAAAAAA );
+        }
+        if ( nVars > 1 )
+        {
+            pStore[2*1+0] = Kit_WordCountOnes( pTruth[0] & 0x33333333 );
+            pStore[2*1+1] = Kit_WordCountOnes( pTruth[0] & 0xCCCCCCCC );
+        }
+        if ( nVars > 2 )
+        {
+            pStore[2*2+0] = Kit_WordCountOnes( pTruth[0] & 0x0F0F0F0F );
+            pStore[2*2+1] = Kit_WordCountOnes( pTruth[0] & 0xF0F0F0F0 );
+        }
+        if ( nVars > 3 )
+        {
+            pStore[2*3+0] = Kit_WordCountOnes( pTruth[0] & 0x00FF00FF );
+            pStore[2*3+1] = Kit_WordCountOnes( pTruth[0] & 0xFF00FF00 );
+        }
+        if ( nVars > 4 )
+        {
+            pStore[2*4+0] = Kit_WordCountOnes( pTruth[0] & 0x0000FFFF );
+            pStore[2*4+1] = Kit_WordCountOnes( pTruth[0] & 0xFFFF0000 );
+        }
+        return;
+    }
+    // nVars >= 6
+    // count 1's for all other variables
+    for ( k = 0; k < nWords; k++ )
+    {
+        Counter = Kit_WordCountOnes( pTruth[k] );
+        for ( i = 5; i < nVars; i++ )
+            if ( k & (1 << (i-5)) )
+                pStore[2*i+1] += Counter;
+            else
+                pStore[2*i+0] += Counter;
+    }
+    // count 1's for the first five variables
+    for ( k = 0; k < nWords/2; k++ )
+    {
+        pStore[2*0+0] += Kit_WordCountOnes( (pTruth[0] & 0x55555555) | ((pTruth[1] & 0x55555555) <<  1) );
+        pStore[2*0+1] += Kit_WordCountOnes( (pTruth[0] & 0xAAAAAAAA) | ((pTruth[1] & 0xAAAAAAAA) >>  1) );
+        pStore[2*1+0] += Kit_WordCountOnes( (pTruth[0] & 0x33333333) | ((pTruth[1] & 0x33333333) <<  2) );
+        pStore[2*1+1] += Kit_WordCountOnes( (pTruth[0] & 0xCCCCCCCC) | ((pTruth[1] & 0xCCCCCCCC) >>  2) );
+        pStore[2*2+0] += Kit_WordCountOnes( (pTruth[0] & 0x0F0F0F0F) | ((pTruth[1] & 0x0F0F0F0F) <<  4) );
+        pStore[2*2+1] += Kit_WordCountOnes( (pTruth[0] & 0xF0F0F0F0) | ((pTruth[1] & 0xF0F0F0F0) >>  4) );
+        pStore[2*3+0] += Kit_WordCountOnes( (pTruth[0] & 0x00FF00FF) | ((pTruth[1] & 0x00FF00FF) <<  8) );
+        pStore[2*3+1] += Kit_WordCountOnes( (pTruth[0] & 0xFF00FF00) | ((pTruth[1] & 0xFF00FF00) >>  8) );
+        pStore[2*4+0] += Kit_WordCountOnes( (pTruth[0] & 0x0000FFFF) | ((pTruth[1] & 0x0000FFFF) << 16) );
+        pStore[2*4+1] += Kit_WordCountOnes( (pTruth[0] & 0xFFFF0000) | ((pTruth[1] & 0xFFFF0000) >> 16) );
+        pTruth += 2;
+    }
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    [Canonicize the truth table.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned Kit_TruthHash( unsigned * pIn, int nWords )
+{
+    // The 1,024 smallest prime numbers used to compute the hash value
+    // http://www.math.utah.edu/~alfeld/math/primelist.html
+    static int HashPrimes[1024] = { 2, 3, 5, 
+    7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 
+    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 
+    193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 
+    293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 
+    409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 
+    521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 
+    641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 
+    757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 
+    881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 
+    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 
+    1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 
+    1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 
+    1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 
+    1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 
+    1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 
+    1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 
+    1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 
+    1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 
+    1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 
+    2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 
+    2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 
+    2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 
+    2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 
+    2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 
+    2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 
+    2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 
+    2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 
+    2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 
+    3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 
+    3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 
+    3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 
+    3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 
+    3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 
+    3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 
+    3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 
+    3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 
+    3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 
+    4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 
+    4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 
+    4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 
+    4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 
+    4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 
+    4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 
+    4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 
+    4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 
+    5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 
+    5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 
+    5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 
+    5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 
+    5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 
+    5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 
+    5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 
+    5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 
+    6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 
+    6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 
+    6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 
+    6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 
+    6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 
+    6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 
+    6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 
+    6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 
+    6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 
+    7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 
+    7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 
+    7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 
+    7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 
+    7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 
+    7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 
+    7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 
+    8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 
+    8147, 8161 };
+    int i;
+    unsigned uHashKey;
+    assert( nWords <= 1024 );
+    uHashKey = 0;
+    for ( i = 0; i < nWords; i++ )
+        uHashKey ^= HashPrimes[i] * pIn[i];
+    return uHashKey;
+}
+
+ 
+/**Function*************************************************************
+
+  Synopsis    [Canonicize the truth table.]
+
+  Description [Returns the phase. ]
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+unsigned Kit_TruthSemiCanonicize( unsigned * pInOut, unsigned * pAux, int nVars, char * pCanonPerm, short * pStore )
+{
+    unsigned * pIn = pInOut, * pOut = pAux, * pTemp;
+    int nWords = Kit_TruthWordNum( nVars );
+    int i, Temp, fChange, Counter, nOnes;//, k, j, w, Limit;
+    unsigned uCanonPhase;
+
+    // canonicize output
+    uCanonPhase = 0;
+    nOnes = Kit_TruthCountOnes(pIn, nVars);
+    if ( (nOnes > nWords * 16) || ((nOnes == nWords * 16) && (pIn[0] & 1)) )
+    {
+        uCanonPhase |= (1 << nVars);
+        Kit_TruthNot( pIn, pIn, nVars );
+    }
+
+    // collect the minterm counts
+    Kit_TruthCountOnesInCofs( pIn, nVars, pStore );
+
+    // canonicize phase
+    for ( i = 0; i < nVars; i++ )
+    {
+        if ( pStore[2*i+0] <= pStore[2*i+1] )
+            continue;
+        uCanonPhase |= (1 << i);
+        Temp = pStore[2*i+0];
+        pStore[2*i+0] = pStore[2*i+1];
+        pStore[2*i+1] = Temp;
+        Kit_TruthChangePhase( pIn, nVars, i );
+    }
+
+//    Kit_PrintHexadecimal( stdout, pIn, nVars );
+//    printf( "\n" );
+
+    // permute
+    Counter = 0;
+    do {
+        fChange = 0;
+        for ( i = 0; i < nVars-1; i++ )
+        {
+            if ( pStore[2*i] <= pStore[2*(i+1)] )
+                continue;
+            Counter++;
+            fChange = 1;
+
+            Temp = pCanonPerm[i];
+            pCanonPerm[i] = pCanonPerm[i+1];
+            pCanonPerm[i+1] = Temp;
+
+            Temp = pStore[2*i];
+            pStore[2*i] = pStore[2*(i+1)];
+            pStore[2*(i+1)] = Temp;
+
+            Temp = pStore[2*i+1];
+            pStore[2*i+1] = pStore[2*(i+1)+1];
+            pStore[2*(i+1)+1] = Temp;
+
+            Kit_TruthSwapAdjacentVars( pOut, pIn, nVars, i );
+            pTemp = pIn; pIn = pOut; pOut = pTemp;
+        }
+    } while ( fChange );
+
+/*
+    Kit_PrintBinary( stdout, &uCanonPhase, nVars+1 ); printf( " : " );
+    for ( i = 0; i < nVars; i++ )
+        printf( "%d=%d/%d  ", pCanonPerm[i], pStore[2*i], pStore[2*i+1] );
+    printf( "  C = %d\n", Counter );
+    Kit_PrintHexadecimal( stdout, pIn, nVars );
+    printf( "\n" );
+*/
+
+/*
+    // process symmetric variable groups
+    uSymms = 0;
+    for ( i = 0; i < nVars-1; i++ )
+    {
+        if ( pStore[2*i] != pStore[2*(i+1)] ) // i and i+1 cannot be symmetric
+            continue;
+        if ( pStore[2*i] != pStore[2*i+1] )
+            continue;
+        if ( Kit_TruthVarsSymm( pIn, nVars, i, i+1 ) )
+            continue;
+        if ( Kit_TruthVarsAntiSymm( pIn, nVars, i, i+1 ) )
+            Kit_TruthChangePhase( pIn, nVars, i+1 );
+    }
+*/
+
+/*
+    // process symmetric variable groups
+    uSymms = 0;
+    for ( i = 0; i < nVars-1; i++ )
+    {
+        if ( pStore[2*i] != pStore[2*(i+1)] ) // i and i+1 cannot be symmetric
+            continue;
+        // i and i+1 can be symmetric
+        // find the end of this group
+        for ( k = i+1; k < nVars; k++ )
+            if ( pStore[2*i] != pStore[2*k] ) 
+                break;
+        Limit = k;
+        assert( i < Limit-1 );
+        // go through the variables in this group
+        for ( j = i + 1; j < Limit; j++ )
+        {
+            // check symmetry
+            if ( Kit_TruthVarsSymm( pIn, nVars, i, j ) )
+            {
+                uSymms |= (1 << j);
+                continue;
+            }
+            // they are phase-unknown
+            if ( pStore[2*i] == pStore[2*i+1] ) 
+            {
+                if ( Kit_TruthVarsAntiSymm( pIn, nVars, i, j ) )
+                {
+                    Kit_TruthChangePhase( pIn, nVars, j );
+                    uCanonPhase ^= (1 << j);
+                    uSymms |= (1 << j);
+                    continue;
+                }
+            }
+
+            // they are not symmetric - move j as far as it goes in the group
+            for ( k = j; k < Limit-1; k++ )
+            {
+                Counter++;
+
+                Temp = pCanonPerm[k];
+                pCanonPerm[k] = pCanonPerm[k+1];
+                pCanonPerm[k+1] = Temp;
+
+                assert( pStore[2*k] == pStore[2*(k+1)] );
+                Kit_TruthSwapAdjacentVars( pOut, pIn, nVars, k );
+                pTemp = pIn; pIn = pOut; pOut = pTemp;
+            }
+            Limit--;
+            j--;
+        }
+        i = Limit - 1;
+    }
+*/
+
+    // swap if it was moved an even number of times
+    if ( Counter & 1 )
+        Kit_TruthCopy( pOut, pIn, nVars );
+    return uCanonPhase;
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/kit_.c b/src/opt/kit/kit_.c
new file mode 100644
index 00000000..5c68ee3c
--- /dev/null
+++ b/src/opt/kit/kit_.c
@@ -0,0 +1,48 @@
+/**CFile****************************************************************
+
+  FileName    [kit_.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [Computation kit.]
+
+  Synopsis    []
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - Dec 6, 2006.]
+
+  Revision    [$Id: kit_.c,v 1.00 2006/12/06 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "kit.h"
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
diff --git a/src/opt/kit/module.make b/src/opt/kit/module.make
new file mode 100644
index 00000000..36beda7a
--- /dev/null
+++ b/src/opt/kit/module.make
@@ -0,0 +1,7 @@
+SRC +=  src/opt/kit/kitBdd.c \
+    src/opt/kit/kitFactor.c \
+    src/opt/kit/kitGraph.c \
+    src/opt/kit/kitHop.c \
+    src/opt/kit/kitIsop.c \
+    src/opt/kit/kitSop.c \
+    src/opt/kit/kitTruth.c