/// <summary>
/// Returns a (deterministic) automaton that accepts the complement of the
/// language of the given automaton.
/// <para/>
/// Complexity: linear in number of states (if already deterministic).
/// </summary>
public static Automaton Complement(Automaton a)
{
a = a.CloneExpandedIfRequired();
a.Determinize();
a.Totalize();
foreach (State p in a.GetNumberedStates())
{
p.accept = !p.accept;
}
a.RemoveDeadTransitions();
return(a);
}
/// <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>
/// Simple, original brics implementation of Determinize()
/// Determinizes the given automaton using the given set of initial states.
/// </summary>
public static void DeterminizeSimple(Automaton a, ISet <State> initialset)
{
int[] points = a.GetStartPoints();
// subset construction
IDictionary <ISet <State>, ISet <State> > sets = new Dictionary <ISet <State>, ISet <State> >();
LinkedList <ISet <State> > worklist = new LinkedList <ISet <State> >();
IDictionary <ISet <State>, State> newstate = new Dictionary <ISet <State>, State>();
sets[initialset] = initialset;
worklist.AddLast(initialset);
a.initial = new State();
newstate[initialset] = a.initial;
while (worklist.Count > 0)
{
ISet <State> s = worklist.First.Value;
worklist.Remove(s);
State r = newstate[s];
foreach (State q in s)
{
if (q.accept)
{
r.accept = true;
break;
}
}
for (int n = 0; n < points.Length; n++)
{
ISet <State> p = new EquatableSet <State>();
foreach (State q in s)
{
foreach (Transition t in q.GetTransitions())
{
if (t.min <= points[n] && points[n] <= t.max)
{
p.Add(t.to);
}
}
}
if (!sets.ContainsKey(p))
{
sets[p] = p;
worklist.AddLast(p);
newstate[p] = new State();
}
State q_ = newstate[p];
int min = points[n];
int max;
if (n + 1 < points.Length)
{
max = points[n + 1] - 1;
}
else
{
max = Character.MAX_CODE_POINT;
}
r.AddTransition(new Transition(min, max, q_));
}
}
a.deterministic = true;
a.ClearNumberedStates();
a.RemoveDeadTransitions();
}
/// <summary>
/// Returns an automaton that accepts the intersection of the languages of the
/// given automata. Never modifies the input automata languages.
/// <para/>
/// Complexity: quadratic in number of states.
/// </summary>
public static Automaton Intersection(Automaton a1, Automaton a2)
{
if (a1.IsSingleton)
{
if (BasicOperations.Run(a2, a1.singleton))
{
return(a1.CloneIfRequired());
}
else
{
return(BasicAutomata.MakeEmpty());
}
}
if (a2.IsSingleton)
{
if (BasicOperations.Run(a1, a2.singleton))
{
return(a2.CloneIfRequired());
}
else
{
return(BasicAutomata.MakeEmpty());
}
}
if (a1 == a2)
{
return(a1.CloneIfRequired());
}
Transition[][] transitions1 = a1.GetSortedTransitions();
Transition[][] transitions2 = a2.GetSortedTransitions();
Automaton c = new Automaton();
LinkedList <StatePair> worklist = new LinkedList <StatePair>();
Dictionary <StatePair, StatePair> newstates = new Dictionary <StatePair, StatePair>();
StatePair p = new StatePair(c.initial, a1.initial, a2.initial);
worklist.AddLast(p);
newstates[p] = p;
while (worklist.Count > 0)
{
p = worklist.First.Value;
worklist.Remove(p);
p.s.accept = p.S1.accept && p.S2.accept;
Transition[] t1 = transitions1[p.S1.number];
Transition[] t2 = transitions2[p.S2.number];
for (int n1 = 0, b2 = 0; n1 < t1.Length; n1++)
{
while (b2 < t2.Length && t2[b2].max < t1[n1].min)
{
b2++;
}
for (int n2 = b2; n2 < t2.Length && t1[n1].max >= t2[n2].min; n2++)
{
if (t2[n2].max >= t1[n1].min)
{
StatePair q = new StatePair(t1[n1].to, t2[n2].to);
StatePair r;
newstates.TryGetValue(q, out r);
if (r == null)
{
q.s = new State();
worklist.AddLast(q);
newstates[q] = q;
r = q;
}
int min = t1[n1].min > t2[n2].min ? t1[n1].min : t2[n2].min;
int max = t1[n1].max < t2[n2].max ? t1[n1].max : t2[n2].max;
p.s.AddTransition(new Transition(min, max, r.s));
}
}
}
}
c.deterministic = a1.deterministic && a2.deterministic;
c.RemoveDeadTransitions();
c.CheckMinimizeAlways();
return(c);
}
/// <summary>
/// Simple, original brics implementation of Determinize()
/// Determinizes the given automaton using the given set of initial states.
/// </summary>
public static void DeterminizeSimple(Automaton a, ISet <State> initialset)
{
int[] points = a.GetStartPoints();
// subset construction
IDictionary <ISet <State>, ISet <State> > sets = new Dictionary <ISet <State>, ISet <State> >();
Queue <ISet <State> > worklist = new Queue <ISet <State> >();// LUCENENET specific - Queue is much more performant than LinkedList
IDictionary <ISet <State>, State> newstate = new Dictionary <ISet <State>, State>();
sets[initialset] = initialset;
worklist.Enqueue(initialset);
a.initial = new State();
newstate[initialset] = a.initial;
while (worklist.Count > 0)
{
ISet <State> s = worklist.Dequeue();
State r = newstate[s];
foreach (State q in s)
{
if (q.accept)
{
r.accept = true;
break;
}
}
for (int n = 0; n < points.Length; n++)
{
ISet <State> p = new JCG.HashSet <State>();
foreach (State q in s)
{
foreach (Transition t in q.GetTransitions())
{
if (t.min <= points[n] && points[n] <= t.max)
{
p.Add(t.to);
}
}
}
if (!sets.ContainsKey(p))
{
sets[p] = p;
worklist.Enqueue(p);
newstate[p] = new State();
}
State q_ = newstate[p];
int min = points[n];
int max;
if (n + 1 < points.Length)
{
max = points[n + 1] - 1;
}
else
{
max = Character.MaxCodePoint;
}
r.AddTransition(new Transition(min, max, q_));
}
}
a.deterministic = true;
a.ClearNumberedStates();
a.RemoveDeadTransitions();
}
/// <summary>
/// Simple, original brics implementation of determinize()
/// Determinizes the given automaton using the given set of initial states.
/// </summary>
public static void DeterminizeSimple(Automaton a, ISet<State> initialset)
{
int[] points = a.StartPoints;
// subset construction
IDictionary<ISet<State>, ISet<State>> sets = new Dictionary<ISet<State>, ISet<State>>();
LinkedList<ISet<State>> worklist = new LinkedList<ISet<State>>();
IDictionary<ISet<State>, State> newstate = new Dictionary<ISet<State>, State>();
sets[initialset] = initialset;
worklist.AddLast(initialset);
a.InitialState = new State();
newstate[initialset] = a.InitialState;
while (worklist.Count > 0)
{
ISet<State> s = worklist.First.Value;
worklist.RemoveFirst();
State r = newstate[s];
foreach (State q in s)
{
if (q.Accept)
{
r.Accept = true;
break;
}
}
for (int n = 0; n < points.Length; n++)
{
ISet<State> p = new HashSet<State>();
foreach (State q in s)
{
foreach (Transition t in q.Transitions)
{
if (t.Min <= points[n] && points[n] <= t.Max)
{
p.Add(t.Dest);
}
}
}
if (!sets.ContainsKey(p))
{
sets[p] = p;
worklist.AddLast(p);
newstate[p] = new State();
}
State q_ = newstate[p];
int min = points[n];
int max;
if (n + 1 < points.Length)
{
max = points[n + 1] - 1;
}
else
{
max = Character.MAX_CODE_POINT;
}
r.AddTransition(new Transition(min, max, q_));
}
}
a.Deterministic = true;
a.ClearNumberedStates();
a.RemoveDeadTransitions();
}
/// <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_Renamed == Character.MIN_CODE_POINT && t.Max_Renamed == Character.MAX_CODE_POINT)
{
return;
}
}
a.Totalize();
// initialize data structures
int[] sigma = a.StartPoints;
State[] states = a.NumberedStates;
int sigmaLen = sigma.Length, statesLen = states.Length;
List<State>[,] reverse = new List<State>[statesLen, sigmaLen];
HashSet<State>[] partition = new HashSet<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<IntPair> pending = new LinkedList<IntPair>();
BitArray pending2 = new BitArray(sigmaLen * statesLen);
BitArray split = new BitArray(statesLen), refine = new BitArray(statesLen), refine2 = new BitArray(statesLen);
for (int q = 0; q < statesLen; q++)
{
splitblock[q] = new List<State>();
partition[q] = new HashSet<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].Size <= active[1, x].Size) ? 0 : 1;
pending.AddLast(new IntPair(j, x));
pending2.Set(x * statesLen + j, true);
}
// process pending until fixed point
int k = 2;
while (pending.Count > 0)
{
IntPair ip = pending.First.Value;
pending.RemoveFirst();
int p = ip.N1;
int x = ip.N2;
pending2.Set(x * statesLen + p, false);
// 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, true);
int j = block[i];
splitblock[j].Add(s);
if (!refine2.Get(j))
{
refine2.Set(j, true);
refine.Set(j, true);
}
}
}
}
}
// refine blocks
for (int j = Number.NextSetBit(refine, 0); j >= 0; j = Number.NextSetBit(refine, j + 1))
{
List<State> sb = splitblock[j];
if (sb.Count < partition[j].Count)
{
HashSet<State> b1 = partition[j];
HashSet<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].Size, ak = active[k, c].Size, ofs = c * statesLen;
if (!pending2.Get(ofs + j) && 0 < aj && aj <= ak)
{
pending2.Set(ofs + j, true);
pending.AddLast(new IntPair(j, c));
}
else
{
pending2.Set(ofs + k, true);
pending.AddLast(new IntPair(k, c));
}
}
k++;
}
refine2.Set(j, false);
foreach (State s in sb)
{
split.Set(s.number, false);
}
sb.Clear();
}
refine.SetAll(false);
}
// 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].Transitions)
{
s.AddTransition(new Transition(t.Min_Renamed, t.Max_Renamed, newstates[t.To.number]));
}
}
a.ClearNumberedStates();
a.RemoveDeadTransitions();
}