/// <summary>
/// Remove unreachable state.
/// </summary>
/// <returns></returns>
private DFATable RemoveUnreachable()
{
// All the state that can be reached from 0.
// Find all reachable states.
Func <int, HashSet <int> > FindReachableClosure = x => {
Stack <int> stack = new Stack <int>();
HashSet <int> closure = new HashSet <int> {
x
};
stack.Push(x);
while (stack.Count() > 0)
{
int s = stack.Pop();
foreach (int t in table[s])
{
if (t != -1 && !closure.Contains(t))
{
stack.Push(t);
closure.Add(t);
}
}
}
return(closure);
};
HashSet <int> startClosure = FindReachableClosure(0);
//
// Helper function to check if this state should be deleted.
// A state should be deleted when
// 1. Starting from 0, there is no way to reach it OR
// 2. Starting from it, there is no way to reach final state.
//
Func <int, bool> IsDeletable = s => {
if (!startClosure.Contains(s))
{
return(true);
}
HashSet <int> reachable = FindReachableClosure(s);
return(reachable.Intersect(finals).Count() == 0);
};
DFATable dfa = new DFATable(map, revMap);
bool[] deleted = new bool[table.Count()];
int[] newId = new int[table.Count()];
// Find all the state to be deleted.
for (int i = 0; i < table.Count(); ++i)
{
deleted[i] = IsDeletable(i);
if (!deleted[i])
{
// Create the new state in the simplified DFA.
newId[i] = dfa.AddState();
}
}
// Copy the transitions.
for (int s = 0; s < table.Count(); ++s)
{
// Is this state deleted?
if (!deleted[s])
{
for (int i = 0; i < table[s].Count(); ++i)
{
int t = table[s][i];
// Is t deleted?
if (t != -1 && !deleted[t])
{
dfa.AddTransition(newId[s], newId[t], revMap[i]);
}
}
}
}
// Set the final states.
foreach (int s in finals)
{
if (!deleted[s])
{
dfa.SetStateFinal(newId[s]);
}
}
return(dfa);
}
/// <summary>
/// Use Hopcroft's Algorithm to simplify this DFATable.
///
/// https://en.wikipedia.org/wiki/DFA_minimization
/// </summary>
/// <returns> A new DFATable. </returns>
private DFATable Hopcroft()
{
// The list of new states.
List <NDState> P = new List <NDState>();
// The stack to be processed.
Stack <NDState> W = new Stack <NDState>();
// Push finals and non-finals.
// P := { F, NF };
// W := { F };
{
NDState F = new NDState(finals);
W.Push(F);
P.Add(F);
NDState NF = new NDState();
for (int i = 0; i < table.Count(); ++i)
{
if (!F.Contains(i))
{
NF.Add(i);
}
}
if (NF.Count() > 0)
{
P.Add(NF);
}
}
while (W.Count() > 0)
{
NDState A = W.Pop();
for (int c = 0; c < revMap.Count(); ++c)
{
// X is the set of states for which a transition on c
// leads to a state in A.
NDState X = new NDState();
for (int i = 0; i < table.Count(); ++i)
{
if (A.Contains(table[i][c]))
{
X.Add(i);
}
}
int PSize = P.Count();
for (int i = 0; i < PSize; ++i)
{
NDState Y = P[i];
NDState I = new NDState(X.Intersect(Y));
if (I.Count() > 0 && I.Count() < Y.Count())
{
// Replace Y with intersec(X, Y) and Y \ X.
Y.ExceptWith(I);
P.Add(I);
// If Y is in W, replace Y with intersec(X, Y) and Y \ X.
// Notice that since object is reference, Y in W has already changed.
if (W.Contains(Y))
{
W.Push(I);
}
else
{
W.Push(I);
W.Push(Y);
}
}
}
}
}
// Make sure that 0 is the start state.
for (int i = 0; i < P.Count(); ++i)
{
if (P[i].Contains(0))
{
NDState tmp = P[0];
P[0] = P[i];
P[i] = tmp;
break;
}
}
// Build the new DFATable.
int[] newId = new int[table.Count()];
DFATable dfa = new DFATable(map, revMap);
for (int i = 0; i < P.Count(); ++i)
{
int x = dfa.AddState();
foreach (int s in P[i])
{
newId[s] = x;
}
if (finals.Contains(P[i].First()))
{
dfa.SetStateFinal(x);
}
}
// Copy the transition.
for (int i = 0; i < P.Count(); ++i)
{
int s = P[i].First();
for (int c = 0; c < revMap.Count(); ++c)
{
if (table[s][c] != -1)
{
dfa.AddTransition(newId[s], newId[table[s][c]], revMap[c]);
}
}
}
return(dfa);
}
/// <summary>
/// Convert NFATable to DFATable.
/// </summary>
/// <returns> A DFATable. </returns>
public DFATable ToDFATable()
{
// Helper function to check if this DFAState is final.
Func <DFAState, bool> IsFinal = x => {
foreach (int s in x)
{
if (finals.Contains(s))
{
return(true);
}
}
return(false);
};
DFATable dfa = new DFATable(map, revMap);
// Map DFAState to the actual state ID in DFATable.
Dictionary <DFAState, int> dict = new Dictionary <DFAState, int>(DFAState.CreateSetComparer());
Stack <DFAState> unmarked = new Stack <DFAState>();
// Initialize the first DFA state.
DFAState closure = FindEpsilonClosure(new HashSet <int> {
0
});
dict.Add(closure, dfa.AddState());
unmarked.Push(closure);
if (IsFinal(closure))
{
dfa.SetStateFinal(dict[closure]);
}
// Build the DFA by simulating NFA.
while (unmarked.Count() > 0)
{
DFAState T = unmarked.Pop();
for (int i = 0; i < revMap.Count(); ++i)
{
// Find move(T, i).
DFAState move = new DFAState();
foreach (int s in T)
{
move.UnionWith(table[s][i]);
}
// U = epsilon-closure(move).
DFAState U = FindEpsilonClosure(move);
if (!dict.ContainsKey(U))
{
// This is a new DFAState.
dict.Add(U, dfa.AddState());
unmarked.Push(U);
if (IsFinal(U))
{
dfa.SetStateFinal(dict[U]);
}
}
// Add transition from T to U with i.
dfa.AddTransition(dict[T], dict[U], revMap[i]);
}
}
return(dfa.Minimize());
}