/// <summary>
/// Returns an automaton that accepts the union of the languages of the given
/// automata.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Union(Automaton a1, Automaton a2)
{
if ((a1.IsSingleton && a2.IsSingleton && a1.singleton.Equals(a2.singleton, StringComparison.Ordinal)) || a1 == a2)
{
return(a1.CloneIfRequired());
}
if (a1 == a2)
{
a1 = a1.CloneExpanded();
a2 = a2.CloneExpanded();
}
else
{
a1 = a1.CloneExpandedIfRequired();
a2 = a2.CloneExpandedIfRequired();
}
State s = new State();
s.AddEpsilon(a1.initial);
s.AddEpsilon(a2.initial);
a1.initial = s;
a1.deterministic = false;
//a1.clearHashCode();
a1.ClearNumberedStates();
a1.CheckMinimizeAlways();
return(a1);
}
/// <summary>
/// Returns a clone of this automaton.
/// </summary>
public virtual object Clone()
{
Automaton a = (Automaton)base.MemberwiseClone();
if (!IsSingleton)
{
Dictionary <State, State> m = new Dictionary <State, State>();
State[] states = GetNumberedStates();
foreach (State s in states)
{
m[s] = new State();
}
foreach (State s in states)
{
State p = m[s];
p.accept = s.accept;
if (s == initial)
{
a.initial = p;
}
foreach (Transition t in s.GetTransitions())
{
p.AddTransition(new Transition(t.min, t.max, m[t.to]));
}
}
}
a.ClearNumberedStates();
return(a);
}
/// <summary>
/// Returns an automaton that accepts the union of the empty string and the
/// language of the given automaton.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Optional(Automaton a)
{
a = a.CloneExpandedIfRequired();
State s = new State();
s.AddEpsilon(a.initial);
s.accept = true;
a.initial = s;
a.deterministic = false;
//a.clearHashCode();
a.ClearNumberedStates();
a.CheckMinimizeAlways();
return(a);
}
/// <summary>
/// Returns an automaton that accepts the Kleene star (zero or more
/// concatenated repetitions) of the language of the given automaton. Never
/// modifies the input automaton language.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Repeat(Automaton a)
{
a = a.CloneExpanded();
State s = new State();
s.accept = true;
s.AddEpsilon(a.initial);
foreach (State p in a.GetAcceptStates())
{
p.AddEpsilon(s);
}
a.initial = s;
a.deterministic = false;
//a.clearHashCode();
a.ClearNumberedStates();
a.CheckMinimizeAlways();
return(a);
}
/// <summary>
/// Reverses the language of the given (non-singleton) automaton while returning
/// the set of new initial states.
/// </summary>
public static ISet <State> Reverse(Automaton a)
{
a.ExpandSingleton();
// reverse all edges
Dictionary <State, ISet <Transition> > m = new Dictionary <State, ISet <Transition> >();
State[] states = a.GetNumberedStates();
ISet <State> accept = new JCG.HashSet <State>();
foreach (State s in states)
{
if (s.Accept)
{
accept.Add(s);
}
}
foreach (State r in states)
{
m[r] = new JCG.HashSet <Transition>();
r.accept = false;
}
foreach (State r in states)
{
foreach (Transition t in r.GetTransitions())
{
m[t.to].Add(new Transition(t.min, t.max, r));
}
}
foreach (State r in states)
{
ISet <Transition> tr = m[r];
r.SetTransitions(tr.ToArray(/*new Transition[tr.Count]*/));
}
// make new initial+final states
a.initial.accept = true;
a.initial = new State();
foreach (State r in accept)
{
a.initial.AddEpsilon(r); // ensures that all initial states are reachable
}
a.deterministic = false;
a.ClearNumberedStates();
return(accept);
}
/// <summary>
/// Returns an automaton that accepts the union of the languages of the given
/// automata.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Union(ICollection <Automaton> l)
{
JCG.HashSet <int> ids = new JCG.HashSet <int>();
foreach (Automaton a in l)
{
ids.Add(a.GetHashCode());
}
bool has_aliases = ids.Count != l.Count;
State s = new State();
foreach (Automaton b in l)
{
if (BasicOperations.IsEmpty(b))
{
continue;
}
Automaton bb = b;
if (has_aliases)
{
bb = bb.CloneExpanded();
}
else
{
bb = bb.CloneExpandedIfRequired();
}
s.AddEpsilon(bb.initial);
}
Automaton a_ = new Automaton
{
initial = s,
deterministic = false
};
//a.clearHashCode();
a_.ClearNumberedStates();
a_.CheckMinimizeAlways();
return(a_);
}
/// <summary>
/// Returns an automaton that accepts the concatenation of the languages of the
/// given automata.
/// <para/>
/// Complexity: linear in number of states.
/// </summary>
public static Automaton Concatenate(Automaton a1, Automaton a2)
{
if (a1.IsSingleton && a2.IsSingleton)
{
return(BasicAutomata.MakeString(a1.singleton + a2.singleton));
}
if (IsEmpty(a1) || IsEmpty(a2))
{
return(BasicAutomata.MakeEmpty());
}
// adding epsilon transitions with the NFA concatenation algorithm
// in this case always produces a resulting DFA, preventing expensive
// redundant determinize() calls for this common case.
bool deterministic = a1.IsSingleton && a2.IsDeterministic;
if (a1 == a2)
{
a1 = a1.CloneExpanded();
a2 = a2.CloneExpanded();
}
else
{
a1 = a1.CloneExpandedIfRequired();
a2 = a2.CloneExpandedIfRequired();
}
foreach (State s in a1.GetAcceptStates())
{
s.accept = false;
s.AddEpsilon(a2.initial);
}
a1.deterministic = deterministic;
//a1.clearHashCode();
a1.ClearNumberedStates();
a1.CheckMinimizeAlways();
return(a1);
}
/// <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.MinCodePoint && t.max == Character.MaxCodePoint)
{
return;
}
}
a.Totalize();
// initialize data structures
int[] sigma = a.GetStartPoints();
State[] states = a.GetNumberedStates();
int sigmaLen = sigma.Length, statesLen = states.Length;
JCG.List <State>[,] reverse = new JCG.List <State> [statesLen, sigmaLen];
ISet <State>[] partition = new JCG.HashSet <State> [statesLen];
JCG.List <State>[] splitblock = new JCG.List <State> [statesLen];
int[] block = new int[statesLen];
StateList[,] active = new StateList[statesLen, sigmaLen];
StateListNode[,] active2 = new StateListNode[statesLen, sigmaLen];
Queue <Int32Pair> pending = new Queue <Int32Pair>(); // LUCENENET specific - Queue is much more performant than LinkedList
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 JCG.List <State>();
partition[q] = new JCG.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++)
{
//JCG.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 JCG.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.Enqueue(new Int32Pair(j, x));
pending2.Set(x * statesLen + j);
}
// process pending until fixed point
int k = 2;
while (pending.Count > 0)
{
Int32Pair ip = pending.Dequeue();
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)
{
JCG.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))
{
JCG.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.Enqueue(new Int32Pair(j, c));
}
else
{
pending2.Set(ofs + k);
pending.Enqueue(new Int32Pair(k, c));
}
}
k++;
}
refine2.Clear(j);
foreach (State s in sb)
{
split.Clear(s.number);
}
sb.Clear();
}
refine.Clear(0, refine.Length);
}
// 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 an automaton that accepts the concatenation of the languages of the
/// given automata.
/// <para/>
/// Complexity: linear in total number of states.
/// </summary>
public static Automaton Concatenate(IList <Automaton> l)
{
if (l.Count == 0)
{
return(BasicAutomata.MakeEmptyString());
}
bool all_singleton = true;
foreach (Automaton a in l)
{
if (!a.IsSingleton)
{
all_singleton = false;
break;
}
}
if (all_singleton)
{
StringBuilder b = new StringBuilder();
foreach (Automaton a in l)
{
b.Append(a.singleton);
}
return(BasicAutomata.MakeString(b.ToString()));
}
else
{
foreach (Automaton a in l)
{
if (BasicOperations.IsEmpty(a))
{
return(BasicAutomata.MakeEmpty());
}
}
JCG.HashSet <int> ids = new JCG.HashSet <int>();
foreach (Automaton a in l)
{
ids.Add(a.GetHashCode());
}
bool has_aliases = ids.Count != l.Count;
Automaton b = l[0];
if (has_aliases)
{
b = b.CloneExpanded();
}
else
{
b = b.CloneExpandedIfRequired();
}
ISet <State> ac = b.GetAcceptStates();
bool first = true;
foreach (Automaton a in l)
{
if (first)
{
first = false;
}
else
{
if (a.IsEmptyString)
{
continue;
}
Automaton aa = a;
if (has_aliases)
{
aa = aa.CloneExpanded();
}
else
{
aa = aa.CloneExpandedIfRequired();
}
ISet <State> ns = aa.GetAcceptStates();
foreach (State s in ac)
{
s.accept = false;
s.AddEpsilon(aa.initial);
if (s.accept)
{
ns.Add(s);
}
}
ac = ns;
}
}
b.deterministic = false;
//b.clearHashCode();
b.ClearNumberedStates();
b.CheckMinimizeAlways();
return(b);
}
}
/// <summary>
/// Adds epsilon transitions to the given automaton. This method adds extra
/// character interval transitions that are equivalent to the given set of
/// epsilon transitions.
/// </summary>
/// <param name="a"> Automaton. </param>
/// <param name="pairs"> Collection of <see cref="StatePair"/> objects representing pairs of
/// source/destination states where epsilon transitions should be
/// added. </param>
public static void AddEpsilons(Automaton a, ICollection <StatePair> pairs)
{
a.ExpandSingleton();
Dictionary <State, JCG.HashSet <State> > forward = new Dictionary <State, JCG.HashSet <State> >();
Dictionary <State, JCG.HashSet <State> > back = new Dictionary <State, JCG.HashSet <State> >();
foreach (StatePair p in pairs)
{
if (!forward.TryGetValue(p.s1, out JCG.HashSet <State> to))
{
to = new JCG.HashSet <State>();
forward[p.s1] = to;
}
to.Add(p.s2);
if (!back.TryGetValue(p.s2, out JCG.HashSet <State> from))
{
from = new JCG.HashSet <State>();
back[p.s2] = from;
}
from.Add(p.s1);
}
// calculate epsilon closure
LinkedList <StatePair> worklist = new LinkedList <StatePair>(pairs);
JCG.HashSet <StatePair> workset = new JCG.HashSet <StatePair>(pairs);
while (worklist.Count > 0)
{
StatePair p = worklist.First.Value;
worklist.Remove(p);
workset.Remove(p);
#pragma warning disable IDE0018 // Inline variable declaration
JCG.HashSet <State> from;
#pragma warning restore IDE0018 // Inline variable declaration
if (forward.TryGetValue(p.s2, out JCG.HashSet <State> to))
{
foreach (State s in to)
{
StatePair pp = new StatePair(p.s1, s);
if (!pairs.Contains(pp))
{
pairs.Add(pp);
forward[p.s1].Add(s);
back[s].Add(p.s1);
worklist.AddLast(pp);
workset.Add(pp);
if (back.TryGetValue(p.s1, out from))
{
foreach (State q in from)
{
StatePair qq = new StatePair(q, p.s1);
if (!workset.Contains(qq))
{
worklist.AddLast(qq);
workset.Add(qq);
}
}
}
}
}
}
}
// add transitions
foreach (StatePair p in pairs)
{
p.s1.AddEpsilon(p.s2);
}
a.deterministic = false;
//a.clearHashCode();
a.ClearNumberedStates();
a.CheckMinimizeAlways();
}