Exact synthesis of majority gates.

5 files changed, 667 insertions, 1 deletions

diff --git a/abclib.dsp b/abclib.dsp
index f07aae07..0fef02ac 100644
--- a/abclib.dsp
+++ b/abclib.dsp
@@ -2019,6 +2019,10 @@ SOURCE=.\src\sat\bmc\bmcLoad.c
 # End Source File
 # Begin Source File
 
+SOURCE=.\src\sat\bmc\bmcMaj.c
+# End Source File
+# Begin Source File
+
 SOURCE=.\src\sat\bmc\bmcMaxi.c
 # End Source File
 # Begin Source File
diff --git a/src/base/abci/abc.c b/src/base/abci/abc.c
index d7cf43ba..5caf8145 100644
--- a/src/base/abci/abc.c
+++ b/src/base/abci/abc.c
@@ -149,6 +149,7 @@ static int Abc_CommandExact                  ( Abc_Frame_t * pAbc, int argc, cha
 static int Abc_CommandBmsStart               ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandBmsStop                ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandBmsPs                  ( Abc_Frame_t * pAbc, int argc, char ** argv );
+static int Abc_CommandMajExact               ( Abc_Frame_t * pAbc, int argc, char ** argv );
 
 static int Abc_CommandLogic                  ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandComb                   ( Abc_Frame_t * pAbc, int argc, char ** argv );
@@ -815,6 +816,7 @@ void Abc_Init( Abc_Frame_t * pAbc )
     Cmd_CommandAdd( pAbc, "Exact synthesis", "bms_start",  Abc_CommandBmsStart,         0 );
     Cmd_CommandAdd( pAbc, "Exact synthesis", "bms_stop",   Abc_CommandBmsStop,          0 );
     Cmd_CommandAdd( pAbc, "Exact synthesis", "bms_ps",     Abc_CommandBmsPs,            0 );
+    Cmd_CommandAdd( pAbc, "Exact synthesis", "majexact",   Abc_CommandMajExact,         0 );
 
     Cmd_CommandAdd( pAbc, "Various",      "logic",         Abc_CommandLogic,            1 );
     Cmd_CommandAdd( pAbc, "Various",      "comb",          Abc_CommandComb,             1 );
@@ -8068,6 +8070,79 @@ usage:
   SeeAlso     []
 
 ***********************************************************************/
+int Abc_CommandMajExact( Abc_Frame_t * pAbc, int argc, char ** argv )
+{
+    extern void Maj_ManExactSynthesis( int nVars, int nNodes, int fUseConst, int fVerbose );
+    int c, nVars = 3, nNodes = 1, fUseConst = 0, fVerbose = 1;
+    Extra_UtilGetoptReset();
+    while ( ( c = Extra_UtilGetopt( argc, argv, "NMcvh" ) ) != EOF )
+    {
+        switch ( c )
+        {
+        case 'N':
+            if ( globalUtilOptind >= argc )
+            {
+                Abc_Print( -1, "Command line switch \"-N\" should be followed by an integer.\n" );
+                goto usage;
+            }
+            nVars = atoi(argv[globalUtilOptind]);
+            globalUtilOptind++;
+            if ( nVars < 0 )
+                goto usage;
+            break;
+        case 'M':
+            if ( globalUtilOptind >= argc )
+            {
+                Abc_Print( -1, "Command line switch \"-M\" should be followed by an integer.\n" );
+                goto usage;
+            }
+            nNodes = atoi(argv[globalUtilOptind]);
+            globalUtilOptind++;
+            if ( nNodes < 0 )
+                goto usage;
+            break;
+        case 'c':
+            fUseConst ^= 1;
+            break;
+        case 'v':
+            fVerbose ^= 1;
+            break;
+        case 'h':
+            goto usage;
+        default:
+            goto usage;
+        }
+    }
+    if ( (nVars & 1) == 0 )
+    {
+        Abc_Print( -1, "Cannot sythesize MAJ gate with an even number of inputs (%d).\n", nVars );
+        return 1;
+    }
+    Maj_ManExactSynthesis( nVars, nNodes, fUseConst, fVerbose );
+    return 0;
+
+usage:
+    Abc_Print( -2, "usage: majexact [-NM <num>] [-cvh]\n" );
+    Abc_Print( -2, "\t           exactly synthesizes N-input MAJ using MAJ3 gates\n" );
+    Abc_Print( -2, "\t-N <num> : the number of input variables [default = %d]\n", nVars );
+    Abc_Print( -2, "\t-M <num> : the number of MAJ3 nodes [default = %d]\n", nNodes );
+    Abc_Print( -2, "\t-c       : toggle using constant fanins [default = %s]\n", fUseConst ? "yes" : "no" );
+    Abc_Print( -2, "\t-v       : toggle verbose printout [default = %s]\n", fVerbose ? "yes" : "no" );
+    Abc_Print( -2, "\t-h       : print the command usage\n" );
+    return 1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
 int Abc_CommandLogic( Abc_Frame_t * pAbc, int argc, char ** argv )
 {
     Abc_Ntk_t * pNtk, * pNtkRes;
diff --git a/src/misc/util/utilTruth.h b/src/misc/util/utilTruth.h
index 1c03d4c7..3a9eb7c1 100644
--- a/src/misc/util/utilTruth.h
+++ b/src/misc/util/utilTruth.h
@@ -332,6 +332,12 @@ static inline void Abc_TtMux( word * pOut, word * pCtrl, word * pIn1, word * pIn
     for ( w = 0; w < nWords; w++ )
         pOut[w] = (pCtrl[w] & pIn1[w]) | (~pCtrl[w] & pIn0[w]);
 }
+static inline void Abc_TtMaj( word * pOut, word * pIn0, word * pIn1, word * pIn2, int nWords )
+{
+    int w;
+    for ( w = 0; w < nWords; w++ )
+        pOut[w] = (pIn0[w] & pIn1[w]) | (pIn0[w] & pIn2[w]) | (pIn1[w] & pIn2[w]);
+}
 static inline int Abc_TtIntersect( word * pIn1, word * pIn2, int nWords, int fCompl )
 {
     int w;
@@ -417,7 +423,24 @@ static inline void Abc_TtConst1( word * pIn1, int nWords )
     for ( w = 0; w < nWords; w++ )
         pIn1[w] = ~(word)0;
 }
- 
+static inline void Abc_TtIthVar( word * pOut, int iVar, int nVars )
+{
+    int k, nWords = Abc_TtWordNum( nVars );
+    if ( iVar < 6 )
+    {
+        for ( k = 0; k < nWords; k++ )
+            pOut[k] = s_Truths6[iVar];
+    }
+    else
+    {
+        for ( k = 0; k < nWords; k++ )
+            if ( k & (1 << (iVar-6)) )
+                pOut[k] = ~(word)0;
+            else
+                pOut[k] = 0;
+    }
+}
+
 /**Function*************************************************************
 
   Synopsis    [Compares Cof0 and Cof1.]
@@ -2339,6 +2362,145 @@ static inline int Abc_TtCheckOutAnd( word t, int i, word * pOut )
     }
     return -1;
 }
+static inline int Abc_TtCheckOutAnd7( word * t, int i, word * pOut )
+{
+    assert( i < 7 );
+    if ( i == 6 )
+    {
+        word c0 = t[0];
+        word c1 = t[1];
+        assert( c0 != c1 );
+        if ( c0 == 0 ) //  F = i * G
+        {
+            if ( pOut ) pOut[0] = pOut[1] = c1;
+            return 0;
+        }
+        if ( c1 == 0 ) //  F = ~i * G
+        {
+            if ( pOut ) pOut[0] = pOut[1] = c0;
+            return 1;
+        }
+        if ( ~c0 == 0 ) //  F = ~i + G
+        {
+            if ( pOut ) pOut[0] = pOut[1] = c1;
+            return 2;
+        }
+        if ( ~c1 == 0 ) //  F = i + G
+        {
+            if ( pOut ) pOut[0] = pOut[1] = c0;
+            return 3;
+        }
+        if ( c0 == ~c1 ) //  F = i # G
+        {
+            if ( pOut ) pOut[0] = pOut[1] = c0;
+            return 4;
+        }
+    }
+    else
+    {
+        int k, Res[2];
+        for ( k = 0; k < 2; k++ )
+            if ( (Res[k] = Abc_TtCheckOutAnd(t[k], i, pOut+k)) == -1 || Res[0] != Res[k] )
+                return -1;
+        return Res[0];
+    }
+    return -1;
+}
+static inline int Abc_TtCheckOutAnd8( word * t, int i, word * pOut )
+{
+    assert( i < 8 );
+    if ( i == 7 )
+    {
+        word * c0 = t;
+        word * c1 = t + 2;
+        assert( c0[0] != c1[0] || c0[1] != c1[1] );
+        if ( c0[0] == 0 && c0[1] == 0 ) //  F = i * G
+        {
+            if ( pOut ) pOut[0] = pOut[2] = c1[0], pOut[1] = pOut[3] = c1[1];
+            return 0;
+        }
+        if ( c1[0] == 0 && c1[1] == 0 ) //  F = ~i * G
+        {
+            if ( pOut ) pOut[0] = pOut[2] = c0[0], pOut[1] = pOut[3] = c0[1];
+            return 1;
+        }
+        if ( ~c0[0] == 0 && ~c0[1] == 0 ) //  F = ~i + G
+        {
+            if ( pOut ) pOut[0] = pOut[2] = c1[0], pOut[1] = pOut[3] = c1[1];
+            return 2;
+        }
+        if ( ~c1[0] == 0 && ~c1[1] == 0 ) //  F = i + G
+        {
+            if ( pOut ) pOut[0] = pOut[2] = c0[0], pOut[1] = pOut[3] = c0[1];
+            return 3;
+        }
+        if ( c0[0] == ~c1[0] && c0[1] == ~c1[1] ) //  F = i # G
+        {
+            if ( pOut ) pOut[0] = pOut[2] = c0[0], pOut[1] = pOut[3] = c0[1];
+            return 4;
+        }
+    }
+    else if ( i == 6 )
+    {
+        int k, Res[2];
+        for ( k = 0; k < 2; k++ )
+            if ( (Res[k] = Abc_TtCheckOutAnd7(t+2*k, i, pOut+2*k)) == -1 || Res[0] != Res[k] )
+                return -1;
+        return Res[0];
+    }
+    else
+    {
+        int k, Res[4];
+        for ( k = 0; k < 4; k++ )
+            if ( (Res[k] = Abc_TtCheckOutAnd(t[k], i, pOut+k)) == -1 || Res[0] != Res[k] )
+                return -1;
+        return Res[0];
+    }
+    return -1;
+}
+static inline word Abc_TtCheckDecOutOne7( word * t, int * piVar, int * pType )
+{
+    int v, Type, Type2; word Out;
+    for ( v = 6; v >= 0; v-- )
+        if ( (Type = Abc_TtCheckOutAnd7(t, v, NULL)) != -1 )
+        {
+            Abc_TtSwapVars( t, 7, v, 6 );
+            Type2 = Abc_TtCheckOutAnd7(t, 6, &Out);
+            assert( Type == Type2 );
+            *piVar = v;
+            *pType = Type;
+            return Out;
+        }
+    return 0;
+}
+static inline word Abc_TtCheckDecOutOne8( word * t, int * piVar1, int * piVar2, int * pType1, int * pType2 )
+{
+    int v, Type1, Type12, Type2, Type22; word Out[2], Out2;
+    for ( v = 7; v >= 0; v-- )
+        if ( (Type1 = Abc_TtCheckOutAnd8(t, v, NULL)) != -1 )
+        {
+            Abc_TtSwapVars( t, 8, v, 7 );
+            Type12 = Abc_TtCheckOutAnd8(t, 7, Out);
+            assert( Type1 == Type12 );
+            *piVar1 = v;
+            *piVar2 = Type1;
+            break;
+        }
+    if ( v == -1 )
+        return 0;
+    for ( v = 6; v >= 0; v-- )
+        if ( (Type2 = Abc_TtCheckOutAnd7(Out, v, NULL)) != -1 && Abc_Lit2Var(Type2) == Abc_Lit2Var(Type1) )
+        {
+            Abc_TtSwapVars( Out, 7, v, 6 );
+            Type22 = Abc_TtCheckOutAnd7(t, 6, &Out2);
+            assert( Type2 == Type22 );
+            *piVar2 = v;
+            *pType2 = Type2;
+            assert( *piVar2 < *piVar1 );
+            return Out2;
+        }
+    return 0;
+}
 
 /**Function*************************************************************
 
@@ -2536,6 +2698,57 @@ static inline void Unm_ManCheckTest()
 }
 
 
+/**Function*************************************************************
+
+  Synopsis    [Truth table evaluation.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline word Abc_TtEvalLut6( word Ins[6], word Lut, int nVars )
+{
+    word Cube, Res = 0; int k, i;
+    for ( k = 0; k < (1<<nVars); k++ )
+    {
+        if ( ((Lut >> k) & 1) == 0 )
+            continue;
+        Cube = ~(word)0;
+        for ( i = 0; i < nVars; i++ )
+            Cube &= ((k >> i) & 1) ? Ins[i] : ~Ins[i];
+    }
+    return Res;
+}
+static inline unsigned Abc_TtEvalLut5( unsigned Ins[5], int Lut, int nVars )
+{
+    unsigned Cube, Res = 0; int k, i;
+    for ( k = 0; k < (1<<nVars); k++ )
+    {
+        if ( ((Lut >> k) & 1) == 0 )
+            continue;
+        Cube = ~(unsigned)0;
+        for ( i = 0; i < nVars; i++ )
+            Cube &= ((k >> i) & 1) ? Ins[i] : ~Ins[i];
+    }
+    return Res;
+}
+static inline int Abc_TtEvalLut4( int Ins[4], int Lut, int nVars )
+{
+    int Cube, Res = 0; int k, i;
+    for ( k = 0; k < (1<<nVars); k++ )
+    {
+        if ( ((Lut >> k) & 1) == 0 )
+            continue;
+        Cube = ~(int)0;
+        for ( i = 0; i < nVars; i++ )
+            Cube &= ((k >> i) & 1) ? Ins[i] : ~Ins[i];
+    }
+    return Res & ~(~0 << (1<<nVars));
+}
+
 
 /**Function*************************************************************
 
diff --git a/src/sat/bmc/bmcMaj.c b/src/sat/bmc/bmcMaj.c
new file mode 100644
index 00000000..d22a38c9
--- /dev/null
+++ b/src/sat/bmc/bmcMaj.c
@@ -0,0 +1,373 @@
+/**CFile****************************************************************
+
+  FileName    [bmcMaj.c]
+
+  SystemName  [ABC: Logic synthesis and verification system.]
+
+  PackageName [SAT-based bounded model checking.]
+
+  Synopsis    [Exact synthesis with majority gates.]
+
+  Author      [Alan Mishchenko]
+  
+  Affiliation [UC Berkeley]
+
+  Date        [Ver. 1.0. Started - October 1, 2017.]
+
+  Revision    [$Id: bmcMaj.c,v 1.00 2017/10/01 00:00:00 alanmi Exp $]
+
+***********************************************************************/
+
+#include "bmc.h"
+#include "misc/util/utilTruth.h"
+#include "sat/glucose/AbcGlucose.h"
+
+ABC_NAMESPACE_IMPL_START
+
+
+////////////////////////////////////////////////////////////////////////
+///                        DECLARATIONS                              ///
+////////////////////////////////////////////////////////////////////////
+
+#define MAJ_NOBJS  32 // Const0 + Const1 + nVars + nNodes
+
+typedef struct Maj_Man_t_ Maj_Man_t;
+struct Maj_Man_t_ 
+{
+    int               nVars;     // inputs
+    int               nNodes;    // internal nodes
+    int               nObjs;     // total objects (2 consts, nVars inputs, nNodes internal nodes)
+    int               nWords;    // the truth table size in 64-bit words
+    int               iVar;      // the next available SAT variable
+    int               fUseConst; // use constant fanins
+    Vec_Wrd_t *       vInfo;     // Const0 + Const1 + nVars + nNodes + Maj(nVars)
+    int               VarMarks[MAJ_NOBJS][3][MAJ_NOBJS]; // variable marks
+    int               VarVals[MAJ_NOBJS+2]; // values of the first 2 + nVars variables
+    Vec_Wec_t *       vOutLits;  // output vars
+    bmcg_sat_solver * pSat;      // SAT solver
+};
+
+static inline word *  Maj_ManTruth( Maj_Man_t * p, int v ) { return Vec_WrdEntryP( p->vInfo, p->nWords * v ); }
+
+////////////////////////////////////////////////////////////////////////
+///                     FUNCTION DEFINITIONS                         ///
+////////////////////////////////////////////////////////////////////////
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Maj_ManValue( int iMint, int nVars )
+{
+    int k, Count = 0;
+    for ( k = 0; k < nVars; k++ )
+        Count += (iMint >> k) & 1;
+    return (int)(Count > nVars/2);
+}
+Vec_Wrd_t * Maj_ManTruthTables( Maj_Man_t * p )
+{
+    Vec_Wrd_t * vInfo = p->vInfo = Vec_WrdStart( p->nWords * (p->nObjs + 1) ); 
+    int i, nMints = Abc_MaxInt( 64, 1 << p->nVars );
+    Abc_TtFill( Maj_ManTruth(p, 1), p->nWords );
+    for ( i = 0; i < p->nVars; i++ )
+        Abc_TtIthVar( Maj_ManTruth(p, i+2), i, p->nVars );
+    for ( i = 0; i < nMints; i++ )
+        if ( Maj_ManValue(i, p->nVars) )
+            Abc_TtSetBit( Maj_ManTruth(p, p->nObjs), i );
+    //Dau_DsdPrintFromTruth( Maj_ManTruth(p, p->nObjs), p->nVars );
+    return vInfo;
+}
+int Maj_ManMarkup( Maj_Man_t * p )
+{
+    int i, k, j;
+    p->iVar = 1;
+    assert( p->nObjs <= MAJ_NOBJS );
+    // make exception for the first node
+    i = p->nVars + 2;
+    for ( k = 0; k < 3; k++ )
+    {
+        j = 4-k;
+        Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) );
+        p->VarMarks[i][k][j] = p->iVar++;
+    }
+    // assign variables for other nodes
+    for ( i = p->nVars + 3; i < p->nObjs; i++ )
+    {
+        for ( k = 0; k < 3; k++ )
+        {
+            for ( j = (p->fUseConst && k == 2) ? 0 : 2; j < i - k; j++ )
+            {
+                Vec_WecPush( p->vOutLits, j, Abc_Var2Lit(p->iVar, 0) );
+                p->VarMarks[i][k][j] = p->iVar++;
+            }
+        }
+    }
+    //printf( "The number of parameter variables = %d.\n", p->iVar );
+    return p->iVar;
+    // printout
+    for ( i = p->nVars + 2; i < p->nObjs; i++ )
+    {
+        printf( "Node %d\n", i );
+        for ( j = 0; j < p->nObjs; j++ )
+        {
+            for ( k = 0; k < 3; k++ )
+                printf( "%2d ", p->VarMarks[i][k][j] );
+            printf( "\n" );
+        }
+    }
+    return p->iVar;
+}
+Maj_Man_t * Maj_ManAlloc( int nVars, int nNodes, int fUseConst )
+{
+    Maj_Man_t * p = ABC_CALLOC( Maj_Man_t, 1 );
+    p->nVars      = nVars;
+    p->nNodes     = nNodes;
+    p->nObjs      = 2 + nVars + nNodes;
+    p->fUseConst  = fUseConst;
+    p->nWords     = Abc_TtWordNum(nVars);
+    p->vOutLits   = Vec_WecStart( p->nObjs );
+    p->iVar       = Maj_ManMarkup( p );
+    p->VarVals[1] = 1;
+    p->vInfo      = Maj_ManTruthTables( p );
+    p->pSat       = bmcg_sat_solver_start();
+    bmcg_sat_solver_set_nvars( p->pSat, p->iVar );
+    return p;
+}
+void Maj_ManFree( Maj_Man_t * p )
+{
+    bmcg_sat_solver_stop( p->pSat );
+    Vec_WrdFree( p->vInfo );
+    Vec_WecFree( p->vOutLits );
+    ABC_FREE( p );
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+static inline int Maj_ManFindFanin( Maj_Man_t * p, int i, int k )
+{
+    int j, Count = 0, iVar = -1;
+    for ( j = 0; j < p->nObjs; j++ )
+        if ( p->VarMarks[i][k][j] && bmcg_sat_solver_read_cex_varvalue(p->pSat, p->VarMarks[i][k][j]) )
+        {
+            iVar = j;
+            Count++;
+        }
+    assert( Count == 1 );
+    return iVar;
+}
+static inline int Maj_ManEval( Maj_Man_t * p )
+{
+    int i, k, iMint; word * pFanins[3];
+    for ( i = p->nVars + 2; i < p->nObjs; i++ )
+    {
+        for ( k = 0; k < 3; k++ )
+            pFanins[k] = Maj_ManTruth( p, Maj_ManFindFanin(p, i, k) );
+        Abc_TtMaj( Maj_ManTruth(p, i), pFanins[0], pFanins[1], pFanins[2], p->nWords );
+    }
+    iMint = Abc_TtFindFirstDiffBit( Maj_ManTruth(p, p->nObjs-1), Maj_ManTruth(p, p->nObjs), p->nWords );
+    return iMint;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Maj_ManPrintSolution( Maj_Man_t * p )
+{
+    int i, k, iVar;
+    printf( "Realization of %d-input majority using %d MAJ3 gates:\n", p->nVars, p->nNodes );
+    for ( i = p->nVars + 2; i < p->nObjs; i++ )
+    {
+        printf( "%02d = MAJ(", i-2 );
+        for ( k = 0; k < 3; k++ )
+        {
+            iVar = Maj_ManFindFanin( p, i, k );
+            if ( iVar >= 2 && iVar < p->nVars + 2 )
+                printf( " %c", 'a'+iVar-2 );
+            else if ( iVar < 2 )
+                printf( " %d", iVar );
+            else
+                printf( " %02d", iVar-2 );
+        }
+        printf( " )\n" );
+    }
+}
+
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+int Maj_ManAddCnfStart( Maj_Man_t * p )
+{
+    int pLits[MAJ_NOBJS], pLits2[2], i, j, k, n, m;
+    // input constraints
+    for ( i = p->nVars + 2; i < p->nObjs; i++ )
+    {
+        for ( k = 0; k < 3; k++ )
+        {
+            int nLits = 0;
+            for ( j = 0; j < p->nObjs; j++ )
+                if ( p->VarMarks[i][k][j] )
+                    pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 0 );
+            assert( nLits > 0 );
+            // input uniqueness
+            if ( !bmcg_sat_solver_addclause( p->pSat, pLits, nLits ) )
+                return 0;
+            for ( n = 0;   n < nLits; n++ )
+            for ( m = n+1; m < nLits; m++ )
+            {
+                pLits2[0] = Abc_LitNot(pLits[n]);
+                pLits2[1] = Abc_LitNot(pLits[m]);
+                if ( !bmcg_sat_solver_addclause( p->pSat, pLits2, 2 ) )
+                    return 0;
+            }
+            if ( k == 2 )
+                break;
+            // symmetry breaking
+            for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] )
+            for ( n = j; n < p->nObjs; n++ ) if ( p->VarMarks[i][k+1][n] )
+            {
+                pLits2[0] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 );
+                pLits2[1] = Abc_Var2Lit( p->VarMarks[i][k+1][n], 1 );
+                if ( !bmcg_sat_solver_addclause( p->pSat, pLits2, 2 ) )
+                    return 0;
+            }
+        }
+    }
+    // outputs should be used
+    for ( i = 2; i < p->nObjs - 1; i++ )
+    {
+        Vec_Int_t * vArray = Vec_WecEntry(p->vOutLits, i);
+        assert( Vec_IntSize(vArray) > 0 );
+        if ( !bmcg_sat_solver_addclause( p->pSat, Vec_IntArray(vArray), Vec_IntSize(vArray) ) )
+            return 0;
+    }
+    return 1;
+}
+int Maj_ManAddCnf( Maj_Man_t * p, int iMint )
+{
+    // save minterm values
+    int i, k, n, j, Value = Maj_ManValue(iMint, p->nVars);
+    for ( i = 0; i < p->nVars; i++ )
+        p->VarVals[i+2] = (iMint >> i) & 1;
+    bmcg_sat_solver_set_nvars( p->pSat, p->iVar + 4*p->nNodes );
+    //printf( "Adding clauses for minterm %d.\n", iMint );
+    for ( i = p->nVars + 2; i < p->nObjs; i++ )
+    {
+        // fanin connectivity
+        int iBaseSatVarI = p->iVar + 4*(i - p->nVars - 2);
+        for ( k = 0; k < 3; k++ )
+        {
+            int nLits2 = 0;
+            for ( j = 0; j < p->nObjs; j++ ) if ( p->VarMarks[i][k][j] )
+            {
+                int iBaseSatVarJ = p->iVar + 4*(j - p->nVars - 2);
+                for ( n = 0; n < 2; n++ )
+                {
+                    int pLits[3], nLits = 0;
+                    pLits[nLits++] = Abc_Var2Lit( p->VarMarks[i][k][j], 1 );
+                    pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + k, n );
+                    if ( j >= p->nVars + 2 )
+                        pLits[nLits++] = Abc_Var2Lit( iBaseSatVarJ + 3, !n );
+                    else if ( p->VarVals[j] == n )
+                        continue;
+                    if ( !bmcg_sat_solver_addclause( p->pSat, pLits, nLits ) )
+                        return 0;
+                }
+            }
+        }
+        // node functionality
+        for ( n = 0; n < 2; n++ )
+        {
+            if ( i == p->nObjs - 1 && n == Value )
+                continue;
+            for ( k = 0; k < 3; k++ )
+            {
+                int pLits[3], nLits = 0;
+                if ( k != 0 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 0, n );
+                if ( k != 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 1, n );
+                if ( k != 2 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 2, n );
+                if ( i != p->nObjs - 1 ) pLits[nLits++] = Abc_Var2Lit( iBaseSatVarI + 3, !n );
+                assert( nLits <= 3 );
+                if ( !bmcg_sat_solver_addclause( p->pSat, pLits, nLits ) )
+                    return 0;
+            }
+        }
+    }
+    p->iVar += 4*p->nNodes;
+    return 1;
+}
+void Maj_ManExactSynthesis( int nVars, int nNodes, int fUseConst, int fVerbose )
+{
+    int i, iMint = 0;
+    abctime clkTotal = Abc_Clock();
+    Maj_Man_t * p = Maj_ManAlloc( nVars, nNodes, fUseConst );
+    int status = Maj_ManAddCnfStart( p );
+    assert( status );
+    printf( "Running exact synthesis for %d-input majority with %d MAJ3 gates...\n", p->nVars, p->nNodes );
+    for ( i = 0; iMint != -1; i++ )
+    {
+        abctime clk = Abc_Clock();
+        if ( !Maj_ManAddCnf( p, iMint ) )
+            break;
+        status = bmcg_sat_solver_solve( p->pSat, NULL, 0 );
+        if ( fVerbose )
+        {
+            printf( "Iter %3d : ", i );
+            printf( "Vars = %5d  ", p->iVar );
+            printf( "Clauses = %5d  ", bmcg_sat_solver_clausenum(p->pSat) );
+            printf( "Conflicts = %7d  ", bmcg_sat_solver_conflictnum(p->pSat) );
+            Abc_PrintTime( 1, "Time", Abc_Clock() - clk );
+        }
+        if ( status == GLUCOSE_UNSAT )
+        {
+            printf( "The problem has no solution.\n" );
+            break;
+        }
+        iMint = Maj_ManEval( p );
+    }
+    if ( iMint == -1 )
+        Maj_ManPrintSolution( p );
+    Maj_ManFree( p );
+    Abc_PrintTime( 1, "Total runtime", Abc_Clock() - clkTotal );
+}
+
+////////////////////////////////////////////////////////////////////////
+///                       END OF FILE                                ///
+////////////////////////////////////////////////////////////////////////
+
+
+ABC_NAMESPACE_IMPL_END
+
diff --git a/src/sat/bmc/module.make b/src/sat/bmc/module.make
index a88db8dd..94fb27cc 100644
--- a/src/sat/bmc/module.make
+++ b/src/sat/bmc/module.make
@@ -22,6 +22,7 @@ SRC +=    src/sat/bmc/bmcBCore.c \
     src/sat/bmc/bmcICheck.c \
     src/sat/bmc/bmcInse.c \
     src/sat/bmc/bmcLoad.c \
+    src/sat/bmc/bmcMaj.c \
     src/sat/bmc/bmcMaxi.c \
     src/sat/bmc/bmcMesh.c \
     src/sat/bmc/bmcMesh2.c \