public override StateFormula existentialNormalForm()
{
// AX phi = NOT E (X NOT phi)
StateFormula e_operand = operand.existentialNormalForm();
StateFormula not_phi = new SNot(e_operand);
StateFormula exists_next = new SENext(not_phi);
return(new SNot(exists_next));
}
public override StateFormula existentialNormalForm()
{
// AG phi = NOT EG (NOT phi)
StateFormula e_operand = operand.existentialNormalForm();
StateFormula not_phi = new SNot(e_operand);
StateFormula exists_always = new SEAlways(not_phi);
return(new SNot(exists_always));
}
public override StateFormula existentialNormalForm()
{
// AG phi = NOT EF (NOT phi) = NOT E (true U (NOT phi))
StateFormula e_operand = operand.existentialNormalForm();
StateFormula not_phi = new SNot(e_operand);
StateFormula true_state = new SBoolean(true);
StateFormula exists_until = new SEUntil(true_state, not_phi);
return(new SNot(exists_until));
}
public override StateFormula existentialNormalForm()
{
StateFormula e_left = left.existentialNormalForm();
StateFormula e_right = right.existentialNormalForm();
// a OR b = NOT ((NOT a) AND (NOT b))
e_left = new SNot(e_left);
e_right = new SNot(e_right);
StateFormula and = new SAnd(e_left, e_right);
return(new SNot(and));
}
public override StateFormula existentialNormalForm()
{
// E(p W w) = NE((Nw) U (Np AND Nw))
StateFormula not_right1 = new SNot(right);
StateFormula not_right2 = new SNot(right);
StateFormula not_left = new SNot(left);
StateFormula and = new SAnd(not_left, not_right2);
StateFormula exists_until = new SEUntil(not_right1, and);
StateFormula not_exists_until = new SNot(exists_until);
return(not_exists_until.existentialNormalForm());
}
public override StateFormula existentialNormalForm()
{
// A(p U w) = NOT E(NOT w U (NOT p AND NOT w)) AND NOT EG NOT w
StateFormula not_right1 = new SNot(right);
StateFormula not_right2 = new SNot(right);
StateFormula not_right3 = new SNot(right);
StateFormula not_left = new SNot(left);
StateFormula inner_and = new SAnd(not_left, not_right2);
StateFormula exists_until = new SEUntil(not_right1, inner_and);
StateFormula not_exists_left = new SNot(exists_until);
StateFormula exists_always = new SEAlways(not_right3);
StateFormula not_exists_right = new SNot(exists_always);
StateFormula outer_and = new SAnd(not_exists_left, not_exists_right);
return(outer_and.existentialNormalForm());
}
