public static IAutomaton Consume(ICharSet characters)
{
var builder = new AutomatonBuilder();
var start = builder.AddState();
var end = builder.AddState();
builder.SetStartState(start);
builder.AcceptState(end);
builder.AddTransition(start, characters, end);
return(builder.Build());
}
public static IAutomaton Determinize(this IAutomaton @this)
{
var builder = new AutomatonBuilder();
var newStates = new Dictionary <decimal, int>();
var start = @this.GetEpsilonClosure(@this.StartState);
var queue = new Queue <IEnumerable <int> >();
var transitions = new LinkedList <Tuple <decimal, ICharSet, decimal> >();
queue.Enqueue(start);
while (queue.Any())
{
var source = queue.Dequeue();
var sourceBits = source.ToBits();
if (newStates.ContainsKey(sourceBits))
{
continue;
}
var state = builder.AddState();
newStates[sourceBits] = state;
//define start and end
if (source == start)
{
builder.SetStartState(state);
}
if (source.Any(st => @this.AcceptingStates.Contains(st)))
{
builder.AcceptState(state);
}
//get all possible inputs
var inputs = new List <ICharSet>();
foreach (var st in source)
{
var transitionTargets = @this.TransitionsBySource.GetOrDefault(st);
if (transitionTargets == null)
{
continue;
}
foreach (var lhs in transitionTargets.GetKeys())
{
if (lhs != CharSet.Epsilon)
{
// A \ B
// B \ A
// A ^ B
var distinct = true;
inputs = inputs.SelectMany(rhs =>
{
var first = lhs.Except(rhs);
var second = rhs.Except(lhs);
var third = lhs.Intersect(rhs);
if (third.Any())
{
distinct = false;
}
return(new[] { first, second, third }.Where(a => a.Length > 0));
}).ToList();
if (distinct)
{
inputs.Add(lhs);
}
}
}
}
//find target states (in epsilon closure)
foreach (var c in inputs)
{
var dfaState = new HashSet <int>();
foreach (var st in source)
{
var transition = @this.TransitionsBySource.GetOrDefault(st);
var targets = transition?.ReadSet(c);
if (targets == null)
{
continue;
}
foreach (var target in targets)
{
dfaState.Add(target);
}
}
if (dfaState.Any())
{
var epsilonTarget = @this.GetEpsilonClosure(dfaState.ToArray());
var targetBits = epsilonTarget.ToBits();
transitions.AddLast(new Tuple <decimal, ICharSet, decimal>(sourceBits, c, targetBits));
queue.Enqueue(epsilonTarget);
}
}
}
//add all transitions
foreach (var transition in transitions)
{
var source = newStates[transition.Item1];
var target = newStates[transition.Item3];
builder.AddTransition(source, transition.Item2, target);
}
return(builder.Build());
}
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());
}
