private FiniteAutomaton Minimize()
{
// Algorithm: Table-filling
// must operate on a DFA, or else
var considerations = new Queue <StatePair>();
var allPairs = new List <StatePair>();
var reachableStates = GetReachableStates().ToArray();
#if DEBUG
bool duplicatedStates = reachableStates.Distinct().Count() > reachableStates.Length;
Debug.Assert(!duplicatedStates);
#endif
foreach (var pair in GetAllPairs(reachableStates))
{
allPairs.Add(pair);
bool canBeMarked = CanBeConcludedDistinguishable(pair);
if (canBeMarked)
{
pair.Mark();
}
else
{
considerations.Enqueue(pair);
}
}
while (considerations.Count > 0)
{
var thisPair = considerations.Dequeue();
foreach (char character in alphabet)
{
var nextPair = GetNextPair(thisPair, character);
if (nextPair.State1 == nextPair.State2)
{
continue;
}
var matches = from pair in allPairs
where pair == nextPair
select pair;
Debug.Assert(matches.Count() == 1);
var match = matches.First();
if (match.IsMarked)
{
thisPair.Mark();
break;
}
else if (considerations.Contains(match))
{
match.AddEquivalentPair(thisPair);
}
}
}
var minimizedToDFA = new Dictionary <State, List <State> >();
var dfaToMinimized = new Dictionary <State, State>();
foreach (var dfaState in reachableStates)
{
var equivalentClass = new List <State>();
equivalentClass.Add(dfaState);
var minimizedState = new State();
minimizedToDFA.Add(minimizedState, equivalentClass);
dfaToMinimized.Add(dfaState, minimizedState);
}
foreach (var pair in allPairs)
{
if (!pair.IsMarked)
{
State minimized1, minimized2;
bool success1 = dfaToMinimized.TryGetValue(pair.State1, out minimized1),
success2 = dfaToMinimized.TryGetValue(pair.State2, out minimized2);
Debug.Assert(success1);
Debug.Assert(success2);
List <State> class1, class2;
success1 = minimizedToDFA.TryGetValue(minimized1, out class1);
success2 = minimizedToDFA.TryGetValue(minimized2, out class2);
Debug.Assert(success1);
Debug.Assert(success2);
class1.AddRange(class2);
minimizedToDFA.Remove(minimized2);
dfaToMinimized[pair.State2] = minimized1;
}
}
var newTable = new TransitionTable();
var transitions = table.GetAllTransitions();
foreach (var transition in transitions)
{
char character = transition.Item2;
State dfaCurrent = transition.Item1,
dfaNext = transition.Item3;
bool isIsolated = !reachableStates.Contains(dfaCurrent);
if (isIsolated)
{
continue;
}
State minimizedCurrent = dfaToMinimized[dfaCurrent],
minimizedNext = dfaToMinimized[dfaNext];
bool merged = dfaCurrent != dfaNext && minimizedCurrent == minimizedNext;
if (merged)
{
continue;
}
var nextStates = newTable.GetNextStates(minimizedCurrent, character);
bool duplicate = nextStates.Contains(minimizedNext);
if (!duplicate)
{
newTable.Add(minimizedCurrent, character, minimizedNext);
}
}
var newStates = from equivalence in minimizedToDFA
select equivalence.Key;
var newInitial = dfaToMinimized[initial];
var newAccepting = from equivalence in minimizedToDFA
where acceptings.Contains(equivalence.Value.First())
select equivalence.Key;
return(new FiniteAutomaton(newStates.ToArray(), alphabet.ToArray(), newInitial, newAccepting, newTable));
}
public FiniteAutomaton ToDFA()
{
// Algorithm: Powerset Construction
bool isAlreadyDeterministic = IsDeterministic();
if (isAlreadyDeterministic)
{
return(this);
}
List <State> dfaStates = new List <State>(),
dfaAcceptings = new List <State>();
var nfaStatesComparer = new OrderIndependentStatesComparer();
var nfaToDFA = new Dictionary <IEnumerable <State>, State>(nfaStatesComparer);
var dfaToNFA = new Dictionary <State, IEnumerable <State> >();
State dfaInitial = new State();
var nfaInitialClosure = table.GetInitialEpsilonClosure(initial);
if (HasAcceptingState(nfaInitialClosure))
{
dfaAcceptings.Add(dfaInitial);
}
dfaStates.Add(dfaInitial);
nfaToDFA.Add(nfaInitialClosure, dfaInitial);
dfaToNFA.Add(dfaInitial, nfaInitialClosure);
var dfaTable = new TransitionTable();
var considerations = new Queue <State>(dfaStates);
while (considerations.Count > 0)
{
var dfaState = considerations.Dequeue();
IEnumerable <State> correspondingNFAStates; // It is OK for this to be empty.
bool success = dfaToNFA.TryGetValue(dfaState, out correspondingNFAStates);
Debug.Assert(success);
foreach (char character in alphabet)
{
var nextNFAStates = table.GetNextStates(correspondingNFAStates, character);
State nextDFAState;
success = nfaToDFA.TryGetValue(nextNFAStates, out nextDFAState);
if (!success)
{
nextDFAState = new State();
if (HasAcceptingState(nextNFAStates))
{
dfaAcceptings.Add(nextDFAState);
}
dfaStates.Add(nextDFAState);
nfaToDFA.Add(nextNFAStates, nextDFAState);
dfaToNFA.Add(nextDFAState, nextNFAStates);
considerations.Enqueue(nextDFAState);
}
else
{
Debug.Assert(dfaStates.Contains(nextDFAState));
}
dfaTable.Add(dfaState, character, nextDFAState);
}
}
return(new FiniteAutomaton(dfaStates, alphabet.ToArray(), dfaInitial, dfaAcceptings, dfaTable));
}