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|
/**CFile****************************************************************
FileName [satProof.c]
SystemName [ABC: Logic synthesis and verification system.]
PackageName [SAT solver.]
Synopsis [Proof manipulation procedures.]
Author [Alan Mishchenko]
Affiliation [UC Berkeley]
Date [Ver. 1.0. Started - June 20, 2005.]
Revision [$Id: satProof.c,v 1.4 2005/09/16 22:55:03 casem Exp $]
***********************************************************************/
#include "satSolver.h"
#include "vec.h"
#include "aig.h"
ABC_NAMESPACE_IMPL_START
/*
Proof is represented as a vector of integers.
The first entry is -1.
The clause is represented as an offset in this array.
One clause's entry is <size><label><ant1><ant2>...<antN>
Label is initialized to 0.
Root clauses are 1-based. They are marked by prepending bit 1;
*/
////////////////////////////////////////////////////////////////////////
/// DECLARATIONS ///
////////////////////////////////////////////////////////////////////////
typedef struct Sat_Set_t_ Sat_Set_t;
struct Sat_Set_t_
{
int nEnts;
int Label;
int pEnts[0];
};
static inline int Sat_SetCheck( Vec_Int_t * p, Sat_Set_t * pNode ) { return (int *)pNode > Vec_IntArray(p) && (int *)pNode < Vec_IntLimit(p); }
static inline int Sat_SetId( Vec_Int_t * p, Sat_Set_t * pNode ) { return (int *)pNode - Vec_IntArray(p); }
static inline Sat_Set_t * Sat_SetFromId( Vec_Int_t * p, int i ) { return (Sat_Set_t *)(Vec_IntArray(p) + i); }
static inline int Sat_SetSize( Sat_Set_t * pNode ) { return pNode->nEnts + 2; }
#define Sat_PoolForEachSet( p, pNode, i ) \
for ( i = 1; (i < Vec_IntSize(p)) && ((pNode) = Sat_SetFromId(p, Vec_IntEntry(p,i))); i += Sat_SetSize(pNode) )
#define Sat_SetForEachSet( p, pSet, pNode, i ) \
for ( i = 0; (i < pSet->nEnts) && (((pNode) = ((pSet->pEnts[i] & 1) ? NULL : Sat_SetFromId(p, pSet->pEnts[i]))), 1); i++ )
#define Sat_VecForEachSet( pVec, p, pNode, i ) \
for ( i = 0; (i < Vec_IntSize(pVec)) && ((pNode) = Sat_SetFromId(p, Vec_IntEntry(pVec,i))); i++ )
////////////////////////////////////////////////////////////////////////
/// FUNCTION DEFINITIONS ///
////////////////////////////////////////////////////////////////////////
/**Function*************************************************************
Synopsis [Recursively visits useful proof nodes.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
int Sat_ProofReduceOne( Vec_Int_t * p, Sat_Set_t * pNode, int * pnSize, Vec_Int_t * vStack )
{
Sat_Set_t * pNext;
int i, NodeId;
if ( pNode->Label )
return pNode->Label;
// start with node
pNode->Label = 1;
Vec_IntPush( vStack, Sat_SetId(p, pNode) );
// perform DFS search
while ( Vec_IntSize(vStack) )
{
NodeId = Vec_IntPop( vStack );
if ( NodeId & 1 ) // extrated second time
{
pNode = Sat_SetFromId( p, NodeId ^ 1 );
pNode->Label = *pnSize;
*pnSize += Sat_SetSize(pNode);
// update fanins
Sat_SetForEachSet( p, pNode, pNext, i )
if ( pNext )
pNode->pEnts[i] = pNext->Label;
continue;
}
// extracted first time
// add second time
Vec_IntPush( vStack, NodeId ^ 1 );
// add its anticedents
pNode = Sat_SetFromId( p, NodeId );
Sat_SetForEachSet( p, pNode, pNext, i )
if ( pNext && !pNext->Label )
{
pNext->Label = 1;
Vec_IntPush( vStack, Sat_SetId(p, pNode) ); // add first time
}
}
return pNode->Label;
}
/**Function*************************************************************
Synopsis [Recursively visits useful proof nodes.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
/*
int Sat_ProofReduce_rec( Vec_Int_t * p, Sat_Set_t * pNode, int * pnSize )
{
int * pBeg;
assert( Sat_SetCheck(p, pNode) );
if ( pNode->Label )
return pNode->Label;
for ( pBeg = pNode->pEnts; pBeg < pNode->pEnts + pNode->nEnts; pBeg++ )
if ( !(*pBeg & 1) )
*pBeg = Sat_ProofReduce_rec( p, Sat_SetFromId(p, *pBeg), pnSize );
pNode->Label = *pnSize;
*pnSize += Sat_SetSize(pNode);
return pNode->Label;
}
*/
/**Function*************************************************************
Synopsis [Reduces the proof to contain only roots and their children.]
Description [The result is updated proof and updated roots.]
SideEffects []
SeeAlso []
***********************************************************************/
void Sat_ProofReduce( Vec_Int_t * p, Vec_Int_t * vRoots )
{
int i, nSize = 1;
int * pBeg, * pEnd, * pNew;
Vec_Int_t * vStack;
Sat_Set_t * pNode;
// mark used nodes
vStack = Vec_IntAlloc( 1000 );
Sat_VecForEachSet( vRoots, p, pNode, i )
vRoots->pArray[i] = Sat_ProofReduceOne( p, pNode, &nSize, vStack );
Vec_IntFree( vStack );
// compact proof
pNew = Vec_IntArray(p) + 1;
Sat_PoolForEachSet( p, pNode, i )
{
if ( !pNode->Label )
continue;
assert( pNew - Vec_IntArray(p) == pNode->Label );
pNode->Label = 0;
pBeg = (int *)pNode;
pEnd = pBeg + Sat_SetSize(pNode);
while ( pBeg < pEnd )
*pNew++ = *pBeg++;
}
// report the result
printf( "The proof was reduced from %d to %d (by %6.2f %%)\n",
Vec_IntSize(p), nSize, 100.0 * (Vec_IntSize(p) - nSize) / Vec_IntSize(p) );
assert( pNew - Vec_IntArray(p) == nSize );
Vec_IntShrink( p, nSize );
}
/**Function*************************************************************
Synopsis [Recursively visits useful proof nodes.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Sat_ProofLabel( Vec_Int_t * p, Sat_Set_t * pNode, Vec_Int_t * vUsed, Vec_Int_t * vStack )
{
Sat_Set_t * pNext;
int i, NodeId;
if ( pNode->Label )
return;
// start with node
pNode->Label = 1;
Vec_IntPush( vStack, Sat_SetId(p, pNode) );
// perform DFS search
while ( Vec_IntSize(vStack) )
{
NodeId = Vec_IntPop( vStack );
if ( NodeId & 1 ) // extrated second time
{
Vec_IntPush( vUsed, NodeId ^ 1 );
continue;
}
// extracted first time
// add second time
Vec_IntPush( vStack, NodeId ^ 1 );
// add its anticedents
pNode = Sat_SetFromId( p, NodeId );
Sat_SetForEachSet( p, pNode, pNext, i )
if ( pNext && !pNext->Label )
{
pNext->Label = 1;
Vec_IntPush( vStack, Sat_SetId(p, pNode) ); // add first time
}
}
}
/**Function*************************************************************
Synopsis [Computes UNSAT core.]
Description [The result is the array of root clause indexes.]
SideEffects []
SeeAlso []
***********************************************************************/
Vec_Int_t * Sat_ProofCore( Vec_Int_t * p, int nRoots, int * pBeg, int * pEnd )
{
unsigned * pSeen;
Vec_Int_t * vCore, * vUsed, * vStack;
Sat_Set_t * pNode;
int i;
// collect visited clauses
vUsed = Vec_IntAlloc( 1000 );
vStack = Vec_IntAlloc( 1000 );
while ( pBeg < pEnd )
Sat_ProofLabel( p, Sat_SetFromId(p, *pBeg++), vUsed, vStack );
Vec_IntFree( vStack );
// find the core
vCore = Vec_IntAlloc( 1000 );
pSeen = ABC_CALLOC( unsigned, Aig_BitWordNum(nRoots) );
Sat_VecForEachSet( vUsed, p, pNode, i )
{
pNode->Label = 0;
for ( pBeg = pNode->pEnts; pBeg < pNode->pEnts + pNode->nEnts; pBeg++ )
if ( (*pBeg & 1) && !Aig_InfoHasBit(pBeg, *pBeg>>1) )
{
Aig_InfoSetBit( pBeg, *pBeg>>1 );
Vec_IntPush( vCore, (*pBeg>>1)-1 );
}
}
Vec_IntFree( vUsed );
ABC_FREE( pSeen );
return vCore;
}
/**Function*************************************************************
Synopsis [Performs one resultion step.]
Description [Returns ID of the resolvent if success, and -1 if failure.]
SideEffects []
SeeAlso []
***********************************************************************/
Sat_Set_t * Sat_ProofResolve( Vec_Int_t * p, Sat_Set_t * c1, Sat_Set_t * c2 )
{
int i, k, Id, Var = -1, Count = 0;
// find resolution variable
for ( i = 0; i < c1->nEnts; i++ )
for ( k = 0; k < c2->nEnts; k++ )
if ( (c1->pEnts[i] ^ c2->pEnts[k]) == 1 )
{
Var = (c1->pEnts[i] >> 1);
Count++;
}
if ( Count == 0 )
{
printf( "Cannot find resolution variable\n" );
return NULL;
}
if ( Count > 1 )
{
printf( "Found more than 1 resolution variables\n" );
return NULL;
}
// perform resolution
Id = Vec_IntSize( p );
Vec_IntPush( p, 0 ); // placeholder
Vec_IntPush( p, 0 );
for ( i = 0; i < c1->nEnts; i++ )
{
if ( (c1->pEnts[i] >> 1) == Var )
continue;
for ( k = Id + 2; k < Vec_IntSize(p); k++ )
if ( p->pArray[k] == c1->pEnts[i] )
break;
if ( k == Vec_IntSize(p) )
Vec_IntPush( p, c1->pEnts[i] );
}
for ( i = 0; i < c2->nEnts; i++ )
{
if ( (c2->pEnts[i] >> 1) == Var )
continue;
for ( k = Id + 2; k < Vec_IntSize(p); k++ )
if ( p->pArray[k] == c2->pEnts[i] )
break;
if ( k == Vec_IntSize(p) )
Vec_IntPush( p, c2->pEnts[i] );
}
Vec_IntWriteEntry( p, Id, Vec_IntSize(p) - Id - 2 );
return Sat_SetFromId( p, Id );
}
/**Function*************************************************************
Synopsis [Checks the proof for consitency.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
Sat_Set_t * Sat_ProofCheckGetOne( Vec_Int_t * vClauses, Vec_Int_t * vProof, Vec_Int_t * vResolves, int iAnt )
{
Sat_Set_t * pAnt;
if ( iAnt & 1 )
return Sat_SetFromId( vClauses, iAnt >> 1 );
pAnt = Sat_SetFromId( vProof, iAnt );
return Sat_SetFromId( vResolves, pAnt->Label );
}
/**Function*************************************************************
Synopsis [Checks the proof for consitency.]
Description []
SideEffects []
SeeAlso []
***********************************************************************/
void Sat_ProofCheck( Vec_Int_t * vClauses, Vec_Int_t * vProof, int iRoot )
{
Vec_Int_t * vOrigs, * vStack, * vUsed, * vResolves;
Sat_Set_t * pSet, * pSet0, * pSet1;
int i, k;
// collect original clauses
vOrigs = Vec_IntAlloc( 1000 );
Vec_IntPush( vOrigs, -1 );
Sat_PoolForEachSet( vClauses, pSet, i )
Vec_IntPush( vOrigs, Sat_SetId(vClauses, pSet) );
// collect visited clauses
vUsed = Vec_IntAlloc( 1000 );
vStack = Vec_IntAlloc( 1000 );
Sat_ProofLabel( vProof, Sat_SetFromId(vProof, iRoot), vUsed, vStack );
Vec_IntFree( vStack );
// perform resolution steps
vResolves = Vec_IntAlloc( 1000 );
Vec_IntPush( vResolves, -1 );
Sat_VecForEachSet( vUsed, vProof, pSet, i )
{
pSet0 = Sat_ProofCheckGetOne( vOrigs, vProof, vResolves, pSet->pEnts[0] );
for ( k = 1; k < pSet->nEnts; k++ )
{
pSet1 = Sat_ProofCheckGetOne( vOrigs, vProof, vResolves, pSet->pEnts[k] );
pSet0 = Sat_ProofResolve( vResolves, pSet0, pSet1 );
}
pSet->Label = Sat_SetId( vResolves, pSet0 );
}
// clean the proof
Sat_VecForEachSet( vUsed, vProof, pSet, i )
pSet->Label = 0;
// compare the final clause
if ( pSet0->nEnts > 0 )
printf( "Cound not derive the empty clause\n" );
Vec_IntFree( vResolves );
Vec_IntFree( vUsed );
Vec_IntFree( vOrigs );
}
/**Function*************************************************************
Synopsis [Creates variable map.]
Description [1=A, 2=B, neg=global]
SideEffects []
SeeAlso []
***********************************************************************/
void Sat_ProofVarMapCheck( Vec_Int_t * vClauses, Vec_Int_t * vVarMap )
{
Sat_Set_t * pSet;
int i, k, fSeeA, fSeeB;
// make sure all clauses are either A or B
Sat_PoolForEachSet( vClauses, pSet, i )
{
fSeeA = fSeeB = 0;
for ( k = 0; k < pSet->nEnts; k++ )
{
fSeeA += (Vec_IntEntry(vVarMap, pSet->pEnts[k]) == 1);
fSeeB += (Vec_IntEntry(vVarMap, pSet->pEnts[k]) == 2);
}
if ( fSeeA && fSeeB )
printf( "VarMap error!\n" );
}
}
/**Function*************************************************************
Synopsis [Computes interpolant of the proof.]
Description [Assuming that res vars are recorded, too...]
SideEffects []
SeeAlso []
***********************************************************************/
Aig_Man_t * Sat_ProofInterpolant( Vec_Int_t * vProof, int iRoot, Vec_Int_t * vClauses, Vec_Int_t * vVarMap )
{
Vec_Int_t * vOrigs, * vUsed, * vStack;
Aig_Man_t * pAig;
Sat_Set_t * pSet;
int i;
Sat_ProofVarMapCheck( vClauses, vVarMap );
// collect original clauses
vOrigs = Vec_IntAlloc( 1000 );
Vec_IntPush( vOrigs, -1 );
Sat_PoolForEachSet( vClauses, pSet, i )
Vec_IntPush( vOrigs, Sat_SetId(vClauses, pSet) );
// collect visited clauses
vUsed = Vec_IntAlloc( 1000 );
vStack = Vec_IntAlloc( 1000 );
Sat_ProofLabel( vProof, Sat_SetFromId(vProof, iRoot), vUsed, vStack );
Vec_IntFree( vStack );
// start the AIG
pAig = Aig_ManStart( 10000 );
pAig->pName = Aig_UtilStrsav( "interpol" );
for ( i = 0; i < Vec_IntSize(vVarMap); i++ )
if ( Vec_IntEntry(vVarMap, i) < 0 )
Aig_ObjCreatePi( pAig );
return pAig;
}
////////////////////////////////////////////////////////////////////////
/// END OF FILE ///
////////////////////////////////////////////////////////////////////////
ABC_NAMESPACE_IMPL_END
|
