/// <summary>
/// Adds epsilon transitions to the given automaton. This method adds extra character interval
/// transitions that are equivalent to the given set of epsilon transitions.
/// </summary>
/// <param name="a">The automaton.</param>
/// <param name="pairs">A collection of <see cref="StatePair"/> objects representing pairs of
/// source/destination states where epsilon transitions should be added.</param>
internal static void AddEpsilons(Automaton a, ICollection <StatePair> pairs)
{
a.ExpandSingleton();
var forward = new Dictionary <State, HashSet <State> >();
var back = new Dictionary <State, HashSet <State> >();
foreach (StatePair p in pairs)
{
HashSet <State> to = forward[p.FirstState];
if (to == null)
{
to = new HashSet <State>();
forward.Add(p.FirstState, to);
}
to.Add(p.SecondState);
HashSet <State> from = back[p.SecondState];
if (from == null)
{
from = new HashSet <State>();
back.Add(p.SecondState, from);
}
from.Add(p.FirstState);
}
var worklist = new LinkedList <StatePair>(pairs);
var workset = new HashSet <StatePair>(pairs);
while (worklist.Count != 0)
{
StatePair p = worklist.RemoveAndReturnFirst();
workset.Remove(p);
HashSet <State> to = forward[p.SecondState];
HashSet <State> from = back[p.FirstState];
if (to != null)
{
foreach (State s in to)
{
var pp = new StatePair(p.FirstState, s);
if (!pairs.Contains(pp))
{
pairs.Add(pp);
forward[p.FirstState].Add(s);
back[s].Add(p.FirstState);
worklist.AddLast(pp);
workset.Add(pp);
if (from != null)
{
foreach (State q in from)
{
var qq = new StatePair(q, p.FirstState);
if (!workset.Contains(qq))
{
worklist.AddLast(qq);
workset.Add(qq);
}
}
}
}
}
}
}
// Add transitions.
foreach (StatePair p in pairs)
{
p.FirstState.AddEpsilon(p.SecondState);
}
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
}
/// <summary>
/// Returns an automaton that accepts the intersection of the languages of the given automata.
/// Never modifies the input automata languages.
/// </summary>
/// <param name="a1">The a1.</param>
/// <param name="a2">The a2.</param>
/// <returns></returns>
internal static Automaton Intersection(Automaton a1, Automaton a2)
{
if (a1.IsSingleton)
{
if (a2.Run(a1.Singleton))
{
return(a1.CloneIfRequired());
}
return(BasicAutomata.MakeEmpty());
}
if (a2.IsSingleton)
{
if (a1.Run(a2.Singleton))
{
return(a2.CloneIfRequired());
}
return(BasicAutomata.MakeEmpty());
}
if (a1 == a2)
{
return(a1.CloneIfRequired());
}
Transition[][] transitions1 = Automaton.GetSortedTransitions(a1.GetStates());
Transition[][] transitions2 = Automaton.GetSortedTransitions(a2.GetStates());
var c = new Automaton();
var worklist = new LinkedList <StatePair>();
var newstates = new Dictionary <StatePair, StatePair>();
var p = new StatePair(c.Initial, a1.Initial, a2.Initial);
worklist.AddLast(p);
newstates.Add(p, p);
while (worklist.Count > 0)
{
p = worklist.RemoveAndReturnFirst();
p.S.Accept = p.FirstState.Accept && p.SecondState.Accept;
Transition[] t1 = transitions1[p.FirstState.Number];
Transition[] t2 = transitions2[p.SecondState.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)
{
var 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.Add(q, q);
r = q;
}
char min = t1[n1].Min > t2[n2].Min ? t1[n1].Min : t2[n2].Min;
char max = t1[n1].Max < t2[n2].Max ? t1[n1].Max : t2[n2].Max;
p.S.Transitions.Add(new Transition(min, max, r.S));
}
}
}
}
c.IsDeterministic = a1.IsDeterministic && a2.IsDeterministic;
c.RemoveDeadTransitions();
c.CheckMinimizeAlways();
return(c);
}
