@Override
public BooleanFormula visitAtom(BooleanFormula pAtom, FunctionDeclaration<BooleanFormula> pDecl) {
NonLinearMultiplicationTransformation multiplicationTransformation =
new NonLinearMultiplicationTransformation(fmgrView, fmgr);
BooleanFormula result = (BooleanFormula) fmgrView.visit(pAtom, multiplicationTransformation);
BooleanFormulaManagerView booleanFormulaManager = fmgrView.getBooleanFormulaManager();
BooleanFormula additionalAxioms =
booleanFormulaManager.and(multiplicationTransformation.getAdditionalAxioms());
return fmgrView.makeAnd(result, additionalAxioms);
}
/**
* Transform a non linear multiplication operation into a new linear {@link Formula} and adds it
* to {@link #additionalAxioms}. The returned {@link Formula} represents the multiplication
* opertion's result if that {@link Formula} is satisfied.
*
* @return a {@link Formula} representing the result of the multiplication operation
*/
private Formula transformNonLinearMultiplication(
Formula a, Formula b, FormulaType<?> formulaType) {
BooleanFormulaManagerView bfmgr = fmgrView.getBooleanFormulaManager();
Formula multAux =
fmgr.makeVariable(
formulaType,
TERMINATION_AUX_VARS_PREFIX + "MULT_AUX_VAR_" + ID_GENERATOR.getFreshId());
List<BooleanFormula> cases = Lists.newArrayList();
Formula one = fmgrView.makeNumber(formulaType, 1);
Formula minusOne = fmgrView.makeNumber(formulaType, -1);
Formula zero = fmgrView.makeNumber(formulaType, 0);
BooleanFormula aIsZero = fmgrView.makeEqual(a, zero);
BooleanFormula bIsZero = fmgrView.makeEqual(b, zero);
BooleanFormula factorIsZero = fmgrView.makeOr(aIsZero, bIsZero);
cases.add(fmgrView.makeAnd(factorIsZero, fmgrView.makeEqual(multAux, zero)));
BooleanFormula aIsOne = fmgrView.makeEqual(a, one);
BooleanFormula bIsOne = fmgrView.makeEqual(b, one);
cases.add(fmgrView.makeAnd(bIsOne, fmgrView.makeEqual(multAux, a)));
cases.add(fmgrView.makeAnd(aIsOne, fmgrView.makeEqual(multAux, b)));
// 0 < a < 1, 0 < b < 1, -1 < a < 0, -1 < b < 0, a > 1, ...
BooleanFormula zeroLessALessOne =
bfmgr.and(fmgrView.makeLessThan(zero, a, true), fmgrView.makeLessThan(a, one, true));
BooleanFormula zeroLessBLessOne =
bfmgr.and(fmgrView.makeLessThan(zero, b, true), fmgrView.makeLessThan(b, one, true));
BooleanFormula minusOneLessALessZero =
bfmgr.and(fmgrView.makeLessThan(minusOne, a, true), fmgrView.makeLessThan(a, zero, true));
BooleanFormula minusOneLessBLessZero =
bfmgr.and(fmgrView.makeLessThan(minusOne, b, true), fmgrView.makeLessThan(b, zero, true));
BooleanFormula aGreaterOne = bfmgr.and(fmgrView.makeGreaterThan(a, one, true));
BooleanFormula bGreaterOne = bfmgr.and(fmgrView.makeGreaterThan(b, one, true));
BooleanFormula aLessMinuseOne = bfmgr.and(fmgrView.makeLessThan(a, one, true));
BooleanFormula bLessMinuseOne = bfmgr.and(fmgrView.makeLessThan(b, one, true));
// 0 < multAux < 1, -1 < multAux < 0, multAux > 1, ...
BooleanFormula zeroLessResultLessOne =
bfmgr.and(
fmgrView.makeLessThan(zero, multAux, true),
fmgrView.makeLessThan(multAux, one, true));
BooleanFormula minusOneLessResultLessZero =
bfmgr.and(
fmgrView.makeLessThan(minusOne, multAux, true),
fmgrView.makeLessThan(multAux, zero, true));
BooleanFormula resultGreaterOne = bfmgr.and(fmgrView.makeGreaterThan(multAux, one, true));
BooleanFormula resultLessMinuseOne = bfmgr.and(fmgrView.makeLessThan(multAux, one, true));
BooleanFormula positiveResult = fmgrView.makeGreaterThan(multAux, zero, true);
BooleanFormula negativeResult = fmgrView.makeLessThan(multAux, zero, true);
cases.add(bfmgr.and(zeroLessALessOne, zeroLessBLessOne, zeroLessResultLessOne));
cases.add(bfmgr.and(zeroLessALessOne, minusOneLessBLessZero, minusOneLessResultLessZero));
cases.add(bfmgr.and(zeroLessALessOne, bGreaterOne, positiveResult));
cases.add(bfmgr.and(zeroLessALessOne, bLessMinuseOne, negativeResult));
cases.add(bfmgr.and(minusOneLessALessZero, zeroLessBLessOne, minusOneLessResultLessZero));
cases.add(bfmgr.and(minusOneLessALessZero, minusOneLessBLessZero, zeroLessResultLessOne));
cases.add(bfmgr.and(minusOneLessALessZero, bGreaterOne, negativeResult));
cases.add(bfmgr.and(minusOneLessALessZero, bLessMinuseOne, positiveResult));
cases.add(bfmgr.and(aGreaterOne, zeroLessBLessOne, positiveResult));
cases.add(bfmgr.and(aGreaterOne, minusOneLessBLessZero, negativeResult));
cases.add(bfmgr.and(aGreaterOne, bGreaterOne, resultGreaterOne));
cases.add(bfmgr.and(aGreaterOne, bLessMinuseOne, resultLessMinuseOne));
cases.add(bfmgr.and(aLessMinuseOne, zeroLessBLessOne, negativeResult));
cases.add(bfmgr.and(aLessMinuseOne, minusOneLessBLessZero, positiveResult));
cases.add(bfmgr.and(aLessMinuseOne, bGreaterOne, resultLessMinuseOne));
cases.add(bfmgr.and(aLessMinuseOne, bLessMinuseOne, resultGreaterOne));
additionalAxioms.add(bfmgr.or(cases));
return multAux;
}