public static Automaton RemoveEpsilon(Automaton source)
{
//标记所有输入的边都没有消耗字符的状态
var nfa = new Automaton();
nfa.CaptureNames = source.CaptureNames;
var newStartstate = nfa.AddState();
nfa.StartState = newStartstate;
List <Transition> transitions = new List <Transition>();
var oldToNew = new Dictionary <State, State>
{
[source.StartState] = newStartstate
};
var newToOld = new Dictionary <State, State>()
{
[newStartstate] = source.StartState
};
var epsilonStates = new List <State>();
for (int i = 0; i < nfa.States.Count; ++i)
{
var state = nfa.States[i];
var oldState = newToOld[state];
FindPath(oldState, state, transitions, epsilonStates);
if (oldState.IsFinalState)
{
state.IsFinalState = true;
}
foreach (var trans in transitions)
{
var target = trans.End;
if (!oldToNew.Keys.Contains(target))
{
var newState = nfa.AddState();
oldToNew.Add(target, newState);
newToOld.Add(newState, target);
}
var newTransition = nfa.AddTransition(state, oldToNew[target], trans.TransitionType);
newTransition.Range = trans.Range;
newTransition.Capture = trans.Capture;
newTransition.Index = trans.Index;
}
transitions.Clear();
epsilonStates.Clear();
}
return(nfa);
}
public static Automaton NfaToDfa(Automaton nfa, out MultiValueDictionary <State, State> dfaStatesToNfa)
{
var dfa = new Automaton();
dfa.CaptureNames = nfa.CaptureNames;
var dfaStartState = dfa.AddState();
dfa.StartState = dfaStartState;
var nfaTransitionsToDfa = new MultiValueDictionary <Transition, Transition>();
var transitionClasses = new List <Transition>();
var mergeStates = new HashSet <State>();
dfaStatesToNfa = new MultiValueDictionary <State, State>();
dfaStatesToNfa.Add(dfaStartState, nfa.StartState);
//不动点算法，不能使用 foreach！
for (int i = 0; i < dfa.States.Count; ++i)
{
var curDfaState = dfa.States[i];
var nfaStates = dfaStatesToNfa[curDfaState];
foreach (var nfaState in nfaStates)
{
foreach (var outTransition in nfaState.Output)
{
if (!nfaTransitionsToDfa.Values.SelectMany(transitions => transitions).Contains(outTransition))
{
transitionClasses.Add(outTransition);
nfaTransitionsToDfa.Add(outTransition, outTransition);
}
}
}
foreach (var transitionClass in transitionClasses)
{
var nfaTransitions = nfaTransitionsToDfa[transitionClass];
foreach (var nfaTransition in nfaTransitions)
{
var state = nfaTransition.End;
if (!mergeStates.Contains(state))
{
mergeStates.Add(state);
}
}
mergeStates.OrderBy(state => state);
//mergeStates 是候选的一个 DFA 状态。在这之前，还需要判断：这个候选状态是否已经存在于 DFA 中了？
//var isContained = dfaStatesToNfa.Values.Contains((IReadOnlyCollection<State>)mergeStates);
State newDfaState = null;
foreach (var dfaState in dfaStatesToNfa.Keys)
{
var prevNfaStates = dfaStatesToNfa[dfaState];
if (prevNfaStates.Count == mergeStates.Count &&
prevNfaStates.SequenceEqual(mergeStates))
{
newDfaState = dfaState;
break;
}
}
if (newDfaState == null)
{
newDfaState = dfa.AddState();
dfaStatesToNfa.AddRange(newDfaState, mergeStates);
newDfaState.IsFinalState = mergeStates.Any(state => state.IsFinalState);
}
var dfaTransition = dfa.AddTransition(curDfaState, newDfaState, transitionClass.TransitionType);
dfaTransition.Capture = transitionClass.Capture;
dfaTransition.Range = transitionClass.Range;
dfaTransition.Index = transitionClass.Index;
mergeStates.Clear();
}
transitionClasses.Clear();
nfaTransitionsToDfa.Clear();
}
return(dfa);
}
public static Automaton NfaToDfa(Automaton nfa, out MultiValueDictionary<State, State> dfaStatesToNfa)
{
var dfa = new Automaton();
dfa.CaptureNames = nfa.CaptureNames;
var dfaStartState = dfa.AddState();
dfa.StartState = dfaStartState;
var nfaTransitionsToDfa = new MultiValueDictionary<Transition, Transition>();
var transitionClasses = new List<Transition>();
var mergeStates = new HashSet<State>();
dfaStatesToNfa = new MultiValueDictionary<State, State>();
dfaStatesToNfa.Add(dfaStartState, nfa.StartState);
//不动点算法，不能使用 foreach！
for(int i = 0; i < dfa.States.Count; ++i)
{
var curDfaState = dfa.States[i];
var nfaStates = dfaStatesToNfa[curDfaState];
foreach(var nfaState in nfaStates)
{
foreach(var outTransition in nfaState.Output)
{
if (!nfaTransitionsToDfa.Values.SelectMany(transitions => transitions).Contains(outTransition))
{
transitionClasses.Add(outTransition);
nfaTransitionsToDfa.Add(outTransition, outTransition);
}
}
}
foreach(var transitionClass in transitionClasses)
{
var nfaTransitions = nfaTransitionsToDfa[transitionClass];
foreach(var nfaTransition in nfaTransitions)
{
var state = nfaTransition.End;
if (!mergeStates.Contains(state))
mergeStates.Add(state);
}
mergeStates.OrderBy(state => state);
//mergeStates 是候选的一个 DFA 状态。在这之前，还需要判断：这个候选状态是否已经存在于 DFA 中了？
//var isContained = dfaStatesToNfa.Values.Contains((IReadOnlyCollection<State>)mergeStates);
State newDfaState = null;
foreach(var dfaState in dfaStatesToNfa.Keys)
{
var prevNfaStates = dfaStatesToNfa[dfaState];
if (prevNfaStates.Count == mergeStates.Count &&
prevNfaStates.SequenceEqual(mergeStates))
{
newDfaState = dfaState;
break;
}
}
if(newDfaState == null)
{
newDfaState = dfa.AddState();
dfaStatesToNfa.AddRange(newDfaState, mergeStates);
newDfaState.IsFinalState = mergeStates.Any(state => state.IsFinalState);
}
var dfaTransition = dfa.AddTransition(curDfaState, newDfaState, transitionClass.TransitionType);
dfaTransition.Capture = transitionClass.Capture;
dfaTransition.Range = transitionClass.Range;
dfaTransition.Index = transitionClass.Index;
mergeStates.Clear();
}
transitionClasses.Clear();
nfaTransitionsToDfa.Clear();
}
return dfa;
}
public static Automaton RemoveEpsilon(Automaton source)
{
//标记所有输入的边都没有消耗字符的状态
var nfa = new Automaton();
nfa.CaptureNames = source.CaptureNames;
var newStartstate = nfa.AddState();
nfa.StartState = newStartstate;
List<Transition> transitions = new List<Transition>();
var oldToNew = new Dictionary<State, State>
{
[source.StartState] = newStartstate
};
var newToOld = new Dictionary<State, State>()
{
[newStartstate] = source.StartState
};
var epsilonStates = new List<State>();
for(int i = 0; i < nfa.States.Count; ++i)
{
var state = nfa.States[i];
var oldState = newToOld[state];
FindPath(oldState, state, transitions, epsilonStates);
if (oldState.IsFinalState) state.IsFinalState = true;
foreach (var trans in transitions)
{
var target = trans.End;
if(!oldToNew.Keys.Contains(target))
{
var newState = nfa.AddState();
oldToNew.Add(target, newState);
newToOld.Add(newState, target);
}
var newTransition = nfa.AddTransition(state, oldToNew[target], trans.TransitionType);
newTransition.Range = trans.Range;
newTransition.Capture = trans.Capture;
newTransition.Index = trans.Index;
}
transitions.Clear();
epsilonStates.Clear();
}
return nfa;
}
