/// <summary>
/// Returns a (deterministic) automaton that accepts the intersection of the
/// language of <paramref name="a1"/> and the complement of the language of
/// <paramref name="a2"/>. As a side-effect, the automata may be determinized, if not
/// already deterministic.
/// <para/>
/// Complexity: quadratic in number of states (if already deterministic).
/// </summary>
public static Automaton Minus(Automaton a1, Automaton a2)
{
if (BasicOperations.IsEmpty(a1) || a1 == a2)
{
return(BasicAutomata.MakeEmpty());
}
if (BasicOperations.IsEmpty(a2))
{
return(a1.CloneIfRequired());
}
if (a1.IsSingleton)
{
if (BasicOperations.Run(a2, a1.singleton))
{
return(BasicAutomata.MakeEmpty());
}
else
{
return(a1.CloneIfRequired());
}
}
return(Intersection(a1, a2.Complement()));
}
