/// <summary>
/// Returns an automaton that accepts the union of the languages of the given
/// automata.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Union(Automaton a1, Automaton a2)
{
if ((a1.IsSingleton && a2.IsSingleton && a1.singleton.Equals(a2.singleton, StringComparison.Ordinal)) || a1 == a2)
{
return(a1.CloneIfRequired());
}
if (a1 == a2)
{
a1 = a1.CloneExpanded();
a2 = a2.CloneExpanded();
}
else
{
a1 = a1.CloneExpandedIfRequired();
a2 = a2.CloneExpandedIfRequired();
}
State s = new State();
s.AddEpsilon(a1.initial);
s.AddEpsilon(a2.initial);
a1.initial = s;
a1.deterministic = false;
//a1.clearHashCode();
a1.ClearNumberedStates();
a1.CheckMinimizeAlways();
return(a1);
}
/// <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()));
}
/// <summary>
/// Returns an automaton that accepts the intersection of the languages of the
/// given automata. Never modifies the input automata languages.
/// <para/>
/// Complexity: quadratic in number of states.
/// </summary>
public static Automaton Intersection(Automaton a1, Automaton a2)
{
if (a1.IsSingleton)
{
if (BasicOperations.Run(a2, a1.singleton))
{
return(a1.CloneIfRequired());
}
else
{
return(BasicAutomata.MakeEmpty());
}
}
if (a2.IsSingleton)
{
if (BasicOperations.Run(a1, a2.singleton))
{
return(a2.CloneIfRequired());
}
else
{
return(BasicAutomata.MakeEmpty());
}
}
if (a1 == a2)
{
return(a1.CloneIfRequired());
}
Transition[][] transitions1 = a1.GetSortedTransitions();
Transition[][] transitions2 = a2.GetSortedTransitions();
Automaton c = new Automaton();
LinkedList <StatePair> worklist = new LinkedList <StatePair>();
Dictionary <StatePair, StatePair> newstates = new Dictionary <StatePair, StatePair>();
StatePair p = new StatePair(c.initial, a1.initial, a2.initial);
worklist.AddLast(p);
newstates[p] = p;
while (worklist.Count > 0)
{
p = worklist.First.Value;
worklist.Remove(p);
p.s.accept = p.S1.accept && p.S2.accept;
Transition[] t1 = transitions1[p.S1.number];
Transition[] t2 = transitions2[p.S2.number];
for (int n1 = 0, b2 = 0; n1 < t1.Length; n1++)
{
while (b2 < t2.Length && t2[b2].max < t1[n1].min)
{
b2++;
}
for (int n2 = b2; n2 < t2.Length && t1[n1].max >= t2[n2].min; n2++)
{
if (t2[n2].max >= t1[n1].min)
{
StatePair q = new StatePair(t1[n1].to, t2[n2].to);
StatePair r;
newstates.TryGetValue(q, out r);
if (r == null)
{
q.s = new State();
worklist.AddLast(q);
newstates[q] = q;
r = q;
}
int min = t1[n1].min > t2[n2].min ? t1[n1].min : t2[n2].min;
int max = t1[n1].max < t2[n2].max ? t1[n1].max : t2[n2].max;
p.s.AddTransition(new Transition(min, max, r.s));
}
}
}
}
c.deterministic = a1.deterministic && a2.deterministic;
c.RemoveDeadTransitions();
c.CheckMinimizeAlways();
return(c);
}
