public Dfa <TAlphabet> ToMinimumDfa(bool skipRemovalOfUnreachableStates = false)
{
// First eliminate any state(s) that cannot be reached from the start state
var minimizedStates = skipRemovalOfUnreachableStates
? new Set <int>(_delta.Keys)
: GetReachableStates();
// Use the table filling algorithm to find all the pairs of equivalent states
TriangularPair <int>[] eqStatePairs = GetEquivalentPairs();
// Partition the set of states Q into blocks of mutually equivalent states
Set <int>[] blocksWithEqStates = GetMergedEqSets(eqStatePairs);
Set <int>[] blocksWithSingleState =
minimizedStates.Difference(blocksWithEqStates).Select(state => new Set <int>(new [] { state })).ToArray();
List <Set <int> > blockStates = blocksWithEqStates.Concat(blocksWithSingleState).ToList();
Set <int> startBlockState = null;
List <Set <int> > acceptBlocks = new List <Set <int> >();
// The transition relation of the DFA = (States, Transition)
var blockTrans = new Dictionary <Set <int>, IDictionary <TAlphabet, Set <int> > >();
foreach (var blockState in blockStates)
{
if (blockState.Contains(StartState))
{
startBlockState = blockState;
}
if (blockState.Any(s => _acceptStates.Contains(s)))
{
acceptBlocks.Add(blockState);
}
IDictionary <TAlphabet, Set <int> > transition = new Dictionary <TAlphabet, Set <int> >();
foreach (var label in GetLabels())
{
//int toState = Trans[blockState.First()][label];
if (_delta[blockState.First()].TryGetValue(label, out var toState))
{
Set <int> toBlockState = blockStates.First(block => block.Contains(toState));
transition.Add(label, toBlockState);
}
}
blockTrans.Add(blockState, transition);
}
var renamer = new MinimizedDfaRenamer(blockStates, _renamer);
var minDfaTrans = Rename(renamer, blockTrans);
int minDfaStartState = renamer.ToDfaStateIndex(startBlockState);
Set <int> minDfaAcceptStates = AcceptStates(blockStates, renamer, acceptBlocks);
return(new Dfa <TAlphabet>(minDfaStartState, minDfaAcceptStates, minDfaTrans, renamer));
}
static Set <int> AcceptStates(
IEnumerable <Set <int> > blockStates,
MinimizedDfaRenamer renamer,
List <Set <int> > acceptBlocks)
{
Set <int> acceptStates = new Set <int>();
foreach (Set <int> blockState in blockStates)
{
if (acceptBlocks.Any(finalState => blockState.Equals(finalState)))
{
acceptStates.Add(renamer.ToDfaStateIndex(blockState));
}
}
return(acceptStates);
}
static IDictionary <int, Dictionary <TAlphabet, int> > Rename(
MinimizedDfaRenamer renamer,
IDictionary <Set <int>, IDictionary <TAlphabet, Set <int> > > trans)
{
var newDfaTrans = new SortedDictionary <int, Dictionary <TAlphabet, int> >(); // keys/states are sorted
foreach (KeyValuePair <Set <int>, IDictionary <TAlphabet, Set <int> > > entry in trans)
{
Set <int> blockState = entry.Key;
var newDfaTransRow = new Dictionary <TAlphabet, int>();
foreach (KeyValuePair <TAlphabet, Set <int> > tr in entry.Value)
{
newDfaTransRow.Add(tr.Key, renamer.ToDfaStateIndex(tr.Value));
}
newDfaTrans.Add(renamer.ToDfaStateIndex(blockState), newDfaTransRow);
}
return(newDfaTrans);
}
