public void TestWS1S_Forall_x_Exists_y_x_lt_y()
{
var triv = new TrivialBooleanAlgebra();
var ca = new BDDAlgebra <bool>(triv);
var x = new Variable("x", false);
var y = new Variable("y", false);
var x_lt_y = new WS1SLt <bool>(x, y);
var psi4 = ~(new WS1SExists <bool>(x, new WS1SSingleton <bool>(x) & ~(new WS1SExists <bool>(y, new WS1SSingleton <bool>(y) & (x_lt_y)))));
var aut = psi4.GetAutomaton(ca, x, y);
//aut.ShowGraph("aut");
//accepts only the empty word
Assert.IsTrue(aut.StateCount == 1 && aut.IsFinalState(aut.InitialState) && aut.MoveCount == 0);
}
public void TestWS1S_Forall_x_Exists_y_x_lt_y()
{
var triv = new TrivialBooleanAlgebra();
var ca = new BDDAlgebra<bool>(triv);
var x = new Variable("x", true);
var y = new Variable("y", true);
var x_lt_y = new MSOLt<bool>(x, y);
var aut_x_lt_y = x_lt_y.GetAutomaton(ca);
//aut_x_lt_y.ShowGraph("aut_x_lt_y");
var psi4 = new MSOForall<bool>(x, new MSOExists<bool>(y, (x_lt_y)));
var aut = psi4.GetAutomaton(ca);
//accepts only the empty word
Assert.IsTrue(aut.StateCount == 1 && aut.IsFinalState(aut.InitialState) && aut.MoveCount == 0);
}
public void TestWS1S_Forall_x_Exists_y_x_lt_y()
{
var triv = new TrivialBooleanAlgebra();
var ca = new BDDAlgebra <bool>(triv);
var x = new WS1SVariable <bool>("x");
var y = new WS1SVariable <bool>("y");
// Forall x.Exists y.x < y
var psi4 = ~(x ^ !x & ~(y ^ (x < y)));
var aut = psi4.GetAutomaton(ca, x, y);
//aut.ShowGraph("aut");
//accepts only the empty word
Assert.IsTrue(aut.StateCount == 1 && aut.IsFinalState(aut.InitialState) && aut.MoveCount == 0);
}