/// <summary>
/// Minimizes the given automaton using Hopcroft's algorithm.
/// </summary>
public static void MinimizeHopcroft(Automaton a)
{
a.Determinize();
if (a.initial.numTransitions == 1)
{
Transition t = a.initial.TransitionsArray[0];
if (t.to == a.initial && t.min == Character.MIN_CODE_POINT && t.max == Character.MAX_CODE_POINT)
{
return;
}
}
a.Totalize();
// initialize data structures
int[] sigma = a.GetStartPoints();
State[] states = a.GetNumberedStates();
int sigmaLen = sigma.Length, statesLen = states.Length;
List <State>[,] reverse = new List <State> [statesLen, sigmaLen];
ISet <State>[] partition = new EquatableSet <State> [statesLen];
List <State>[] splitblock = new List <State> [statesLen];
int[] block = new int[statesLen];
StateList[,] active = new StateList[statesLen, sigmaLen];
StateListNode[,] active2 = new StateListNode[statesLen, sigmaLen];
LinkedList <Int32Pair> pending = new LinkedList <Int32Pair>();
OpenBitSet pending2 = new OpenBitSet(sigmaLen * statesLen);
OpenBitSet split = new OpenBitSet(statesLen),
refine = new OpenBitSet(statesLen), refine2 = new OpenBitSet(statesLen);
for (int q = 0; q < statesLen; q++)
{
splitblock[q] = new List <State>();
partition[q] = new EquatableSet <State>();
for (int x = 0; x < sigmaLen; x++)
{
active[q, x] = new StateList();
}
}
// find initial partition and reverse edges
for (int q = 0; q < statesLen; q++)
{
State qq = states[q];
int j = qq.accept ? 0 : 1;
partition[j].Add(qq);
block[q] = j;
for (int x = 0; x < sigmaLen; x++)
{
//List<State>[] r = reverse[qq.Step(sigma[x]).number];
var r = qq.Step(sigma[x]).number;
if (reverse[r, x] == null)
{
reverse[r, x] = new List <State>();
}
reverse[r, x].Add(qq);
}
}
// initialize active sets
for (int j = 0; j <= 1; j++)
{
for (int x = 0; x < sigmaLen; x++)
{
foreach (State qq in partition[j])
{
if (reverse[qq.number, x] != null)
{
active2[qq.number, x] = active[j, x].Add(qq);
}
}
}
}
// initialize pending
for (int x = 0; x < sigmaLen; x++)
{
int j = (active[0, x].Count <= active[1, x].Count) ? 0 : 1;
pending.AddLast(new Int32Pair(j, x));
pending2.Set(x * statesLen + j);
}
// process pending until fixed point
int k = 2;
while (pending.Count > 0)
{
Int32Pair ip = pending.First.Value;
pending.Remove(ip);
int p = ip.N1;
int x = ip.N2;
pending2.Clear(x * statesLen + p);
// find states that need to be split off their blocks
for (StateListNode m = active[p, x].First; m != null; m = m.Next)
{
List <State> r = reverse[m.Q.number, x];
if (r != null)
{
foreach (State s in r)
{
int i = s.number;
if (!split.Get(i))
{
split.Set(i);
int j = block[i];
splitblock[j].Add(s);
if (!refine2.Get(j))
{
refine2.Set(j);
refine.Set(j);
}
}
}
}
}
// refine blocks
for (int j = refine.NextSetBit(0); j >= 0; j = refine.NextSetBit(j + 1))
{
List <State> sb = splitblock[j];
if (sb.Count < partition[j].Count)
{
ISet <State> b1 = partition[j];
ISet <State> b2 = partition[k];
foreach (State s in sb)
{
b1.Remove(s);
b2.Add(s);
block[s.number] = k;
for (int c = 0; c < sigmaLen; c++)
{
StateListNode sn = active2[s.number, c];
if (sn != null && sn.Sl == active[j, c])
{
sn.Remove();
active2[s.number, c] = active[k, c].Add(s);
}
}
}
// update pending
for (int c = 0; c < sigmaLen; c++)
{
int aj = active[j, c].Count, ak = active[k, c].Count, ofs = c * statesLen;
if (!pending2.Get(ofs + j) && 0 < aj && aj <= ak)
{
pending2.Set(ofs + j);
pending.AddLast(new Int32Pair(j, c));
}
else
{
pending2.Set(ofs + k);
pending.AddLast(new Int32Pair(k, c));
}
}
k++;
}
refine2.Clear(j);
foreach (State s in sb)
{
split.Clear(s.number);
}
sb.Clear();
}
refine.Clear(0, refine.Length - 1);
}
// make a new state for each equivalence class, set initial state
State[] newstates = new State[k];
for (int n = 0; n < newstates.Length; n++)
{
State s = new State();
newstates[n] = s;
foreach (State q in partition[n])
{
if (q == a.initial)
{
a.initial = s;
}
s.accept = q.accept;
s.number = q.number; // select representative
q.number = n;
}
}
// build transitions and set acceptance
for (int n = 0; n < newstates.Length; n++)
{
State s = newstates[n];
s.accept = states[s.number].accept;
foreach (Transition t in states[s.number].GetTransitions())
{
s.AddTransition(new Transition(t.min, t.max, newstates[t.to.number]));
}
}
a.ClearNumberedStates();
a.RemoveDeadTransitions();
}
/// <summary>
/// Returns <c>true</c> if the given string is accepted by the automaton.
/// <para/>
/// Complexity: linear in the length of the string.
/// <para/>
/// <b>Note:</b> for full performance, use the <see cref="RunAutomaton"/> class.
/// </summary>
public static bool Run(Automaton a, string s)
{
if (a.IsSingleton)
{
return(s.Equals(a.singleton, StringComparison.Ordinal));
}
if (a.deterministic)
{
State p = a.initial;
for (int i = 0, cp = 0; i < s.Length; i += Character.CharCount(cp))
{
State q = p.Step(cp = Character.CodePointAt(s, i));
if (q == null)
{
return(false);
}
p = q;
}
return(p.accept);
}
else
{
State[] states = a.GetNumberedStates();
LinkedList <State> pp = new LinkedList <State>();
LinkedList <State> pp_other = new LinkedList <State>();
OpenBitSet bb = new OpenBitSet(states.Length);
OpenBitSet bb_other = new OpenBitSet(states.Length);
pp.AddLast(a.initial);
List <State> dest = new List <State>();
bool accept = a.initial.accept;
for (int i = 0, c = 0; i < s.Length; i += Character.CharCount(c))
{
c = Character.CodePointAt(s, i);
accept = false;
pp_other.Clear();
bb_other.Clear(0, bb_other.Length - 1);
foreach (State p in pp)
{
dest.Clear();
p.Step(c, dest);
foreach (State q in dest)
{
if (q.accept)
{
accept = true;
}
if (!bb_other.Get(q.number))
{
bb_other.Set(q.number);
pp_other.AddLast(q);
}
}
}
LinkedList <State> tp = pp;
pp = pp_other;
pp_other = tp;
OpenBitSet tb = bb;
bb = bb_other;
bb_other = tb;
}
return(accept);
}
}