tempest/test/functional/solver/Z3SmtSolverTest.cpp

#include "gtest/gtest.h"
#include "storm-config.h"

#ifdef STORM_HAVE_Z3
#include "src/solver/Z3SmtSolver.h"

TEST(Z3SmtSolver, CheckSat) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::expressions::Variable x = manager->declareBooleanVariable("x");
    storm::expressions::Variable y = manager->declareBooleanVariable("y");
    
	storm::solver::Z3SmtSolver s(*manager);
	storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
	storm::expressions::Expression exprDeMorgan = storm::expressions::iff(!(x && y), !x || !y);
    
	ASSERT_NO_THROW(s.add(exprDeMorgan));
	ASSERT_NO_THROW(result = s.check());
	ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
	ASSERT_NO_THROW(s.reset());
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    
	storm::expressions::Expression exprFormula = a >= manager->integer(0) && a < manager->integer(5) && b > manager->integer(7) && c == (a * b) && b + a > c;
    
	ASSERT_NO_THROW(s.add(exprFormula));
	ASSERT_NO_THROW(result = s.check());
	ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
	ASSERT_NO_THROW(s.reset());
}

TEST(Z3SmtSolver, CheckUnsat) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::expressions::Variable x = manager->declareBooleanVariable("x");
    storm::expressions::Variable y = manager->declareBooleanVariable("y");
    
	storm::solver::Z3SmtSolver s(*manager);
	storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
	storm::expressions::Expression exprDeMorgan = storm::expressions::iff(!(x && y), !x || !y);
    
	ASSERT_NO_THROW(s.add(!exprDeMorgan));
	ASSERT_NO_THROW(result = s.check());
	ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
	ASSERT_NO_THROW(s.reset());
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    
	storm::expressions::Expression exprFormula = a >= manager->rational(2) && a < manager->integer(5) && b > manager->integer(7) && c == (a + b + manager->integer(1)) && b + a > c;
    
	ASSERT_NO_THROW(s.add(exprFormula));
	ASSERT_NO_THROW(result = s.check());
	ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
}

TEST(Z3SmtSolver, Backtracking) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::solver::Z3SmtSolver s(*manager);
    storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
    storm::expressions::Expression expr1 = manager->boolean(true);
    storm::expressions::Expression expr2 = manager->boolean(false);
    storm::expressions::Expression expr3 = manager->boolean(false);
    
    ASSERT_NO_THROW(s.add(expr1));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(s.push());
    ASSERT_NO_THROW(s.add(expr2));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    ASSERT_NO_THROW(s.pop());
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(s.push());
    ASSERT_NO_THROW(s.add(expr2));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    ASSERT_NO_THROW(s.push());
    ASSERT_NO_THROW(s.add(expr3));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    ASSERT_NO_THROW(s.pop(2));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(s.reset());
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    storm::expressions::Expression exprFormula = a >= manager->integer(0) && a < manager->integer(5) && b > manager->integer(7) && c == (a + b - manager->integer(1)) && b + a > c;
    storm::expressions::Expression exprFormula2 = c > a + b + manager->integer(1);
    
    ASSERT_NO_THROW(s.add(exprFormula));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(s.push());
    ASSERT_NO_THROW(s.add(exprFormula2));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    ASSERT_NO_THROW(s.pop());
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
}

TEST(Z3SmtSolver, Assumptions) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::solver::Z3SmtSolver s(*manager);
    storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    storm::expressions::Expression exprFormula = a >= manager->integer(0) && a < manager->integer(5) && b > manager->integer(7) && c == a + b - manager->integer(1) && b + a > c;
    storm::expressions::Variable f2 = manager->declareBooleanVariable("f2");
    storm::expressions::Expression exprFormula2 = storm::expressions::implies(f2, c > a + b + manager->integer(1));
    
    ASSERT_NO_THROW(s.add(exprFormula));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(s.add(exprFormula2));
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(result = s.checkWithAssumptions({f2}));
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    ASSERT_NO_THROW(result = s.check());
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    ASSERT_NO_THROW(result = s.checkWithAssumptions({ !f2 }));
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
}

TEST(Z3SmtSolver, GenerateModel) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::solver::Z3SmtSolver s(*manager);
    storm::solver::SmtSolver::CheckResult result;
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    storm::expressions::Expression exprFormula = a > manager->integer(0) && a < manager->integer(5) && b > manager->integer(7) && c == a + b - manager->integer(1) && b + a > c;
    
    s.add(exprFormula);
    result = s.check();
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Sat);
    std::shared_ptr<storm::solver::SmtSolver::ModelReference> model = s.getModel();
    int_fast64_t aEval = model->getIntegerValue(a);
    int_fast64_t bEval = model->getIntegerValue(b);
    int_fast64_t cEval = model->getIntegerValue(c);
    ASSERT_TRUE(cEval == aEval + bEval - 1);
}

TEST(Z3SmtSolver, AllSat) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::solver::Z3SmtSolver s(*manager);
    storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable x = manager->declareBooleanVariable("x");
    storm::expressions::Variable y = manager->declareBooleanVariable("y");
    storm::expressions::Variable z = manager->declareBooleanVariable("z");
    storm::expressions::Expression exprFormula1 = storm::expressions::implies(x, a > manager->integer(5));
    storm::expressions::Expression exprFormula2 = storm::expressions::implies(y, a < manager->integer(5));
    storm::expressions::Expression exprFormula3 = storm::expressions::implies(z, b < manager->integer(5));
    
    s.add(exprFormula1);
    s.add(exprFormula2);
    s.add(exprFormula3);
    
    std::vector<storm::expressions::SimpleValuation> valuations = s.allSat({x,y});
    
    ASSERT_TRUE(valuations.size() == 3);
    for (int i = 0; i < valuations.size(); ++i) {
        ASSERT_FALSE(valuations[i].getBooleanValue(x) && valuations[i].getBooleanValue(y));
        
        for (int j = i+1; j < valuations.size(); ++j) {
            ASSERT_TRUE((valuations[i].getBooleanValue(x) != valuations[j].getBooleanValue(x)) || (valuations[i].getBooleanValue(y) != valuations[j].getBooleanValue(y)));
        }
    }
}

TEST(Z3SmtSolver, UnsatAssumptions) {
    std::shared_ptr<storm::expressions::ExpressionManager> manager(new storm::expressions::ExpressionManager());
    
    storm::solver::Z3SmtSolver s(*manager);
    storm::solver::SmtSolver::CheckResult result = storm::solver::SmtSolver::CheckResult::Unknown;
    
    storm::expressions::Variable a = manager->declareIntegerVariable("a");
    storm::expressions::Variable b = manager->declareIntegerVariable("b");
    storm::expressions::Variable c = manager->declareIntegerVariable("c");
    storm::expressions::Expression exprFormula = a >= manager->integer(0) && a < manager->integer(5) && b > manager->integer(7) && c == a + b - manager->integer(1) && b + a > c;
    storm::expressions::Variable f2 = manager->declareBooleanVariable("f2");
    storm::expressions::Expression exprFormula2 = storm::expressions::implies(f2, c > a + b + manager->integer(1));
    
    s.add(exprFormula);
    s.add(exprFormula2);
    result = s.checkWithAssumptions({ f2 });
    ASSERT_TRUE(result == storm::solver::SmtSolver::CheckResult::Unsat);
    std::vector<storm::expressions::Expression> unsatCore = s.getUnsatAssumptions();
    ASSERT_EQ(unsatCore.size(), 1);
    ASSERT_TRUE(unsatCore[0].isVariable());
    ASSERT_STREQ("f2", unsatCore[0].getIdentifier().c_str());
}

#endif