public static IAutomaton Minimize(this IAutomaton @this)
{
//prepare NFA automaton to a DFA automaton
var automaton = @this.Determinize();
//mark all distinguishable pairs (unacceptable <-> acceptable)
var stateCount = automaton.StateCount;
var distinguishablePairs = new bool?[stateCount, stateCount];
foreach (var acceptable in automaton.AcceptingStates)
{
foreach (var unacceptable in Enumerable.Range(0, stateCount)
.Except(automaton.AcceptingStates))
{
distinguishablePairs[acceptable, unacceptable] = true;
distinguishablePairs[unacceptable, acceptable] = true;
}
}
//try to mark all others
// Example (#=4)
// 1 X
// 2 X X
// 3 X X X
// 0 1 2
var mergedByState = new Dictionary <int, HashSet <int> >();
var merged = new HashSet <HashSet <int> >();
for (var aIndex = 1; aIndex < stateCount; aIndex++)
{
for (var bIndex = 0; bIndex < aIndex; bIndex++)
{
if (!MarkDistinguishables(distinguishablePairs, automaton, aIndex, bIndex))
{
var list = mergedByState.GetValueOrInsertedDefault(aIndex, mergedByState.GetValueOrInsertedLazyDefault(bIndex, () => new HashSet <int>()));
list.Add(aIndex);
list.Add(bIndex);
merged.Add(list);
}
}
}
var mappings = new Dictionary <int, int>(); //old automaton to new automaton states
var inverseMappings = new Dictionary <int, int>();
//NOW BUILD THE F*****G AUTOMATON!!!
var builder = new AutomatonBuilder();
foreach (var mergedStates in merged)
{
var newState = builder.AddState();
inverseMappings[newState] = mergedStates.First();
foreach (var oldState in mergedStates)
{
mappings[oldState] = newState;
}
}
for (var state = 0; state < automaton.StateCount; state++)
{
if (!mappings.ContainsKey(state))
{
var newState = builder.AddState();
mappings[state] = newState;
inverseMappings[newState] = state;
}
}
//mark starts and ends
builder.SetStartState(mappings[automaton.StartState]);
foreach (var accept in automaton.AcceptingStates)
{
builder.AcceptState(mappings[accept]);
}
//add transitions
foreach (var kv in inverseMappings)
{
var oldState = kv.Value;
var newState = kv.Key;
foreach (var transition in automaton.TransitionsBySource.GetOrDefault(oldState, AutomatonExtensions.EmptyTargets))
{
builder.AddTransition(newState, transition.Key, mappings[transition.First()]);
}
}
//build
return(builder.Build());
}