/// <summary>
/// Accepts between <code>min</code> and <code>max</code> (including both) concatenated
/// repetitions of the language of the given automaton.
/// </summary>
/// <param name="a">The automaton.</param>
/// <param name="min">The minimum concatenated repetitions of the language of the given
/// automaton.</param>
/// <param name="max">The maximum concatenated repetitions of the language of the given
/// automaton.</param>
/// <returns>
/// Returns an automaton that accepts between <code>min</code> and <code>max</code>
/// (including both) concatenated repetitions of the language of the given automaton.
/// </returns>
/// <remarks>
/// Complexity: linear in number of states and in <code>min</code> and <code>max</code>.
/// </remarks>
public static Automaton Repeat(Automaton a, int min, int max)
{
if (min > max)
{
return(BasicAutomata.MakeEmpty());
}
max -= min;
a.ExpandSingleton();
Automaton b;
if (min == 0)
{
b = BasicAutomata.MakeEmptyString();
}
else if (min == 1)
{
b = a.Clone();
}
else
{
var @as = new List <Automaton>();
while (min-- > 0)
{
@as.Add(a);
}
b = BasicOperations.Concatenate(@as);
}
if (max > 0)
{
Automaton d = a.Clone();
while (--max > 0)
{
Automaton c = a.Clone();
foreach (State p in c.GetAcceptStates())
{
p.AddEpsilon(d.Initial);
}
d = c;
}
foreach (State p in b.GetAcceptStates())
{
p.AddEpsilon(d.Initial);
}
b.IsDeterministic = false;
b.ClearHashCode();
b.CheckMinimizeAlways();
}
return(b);
}
/// <summary>
/// Accepts the Kleene star (zero or more concatenated repetitions) of the language of the
/// given automaton. Never modifies the input automaton language.
/// </summary>
/// <param name="a">The automaton.</param>
/// <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.
/// </returns>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
public static Automaton Repeat(Automaton a)
{
a = a.CloneExpanded();
var s = new State();
s.Accept = true;
s.AddEpsilon(a.Initial);
foreach (State p in a.GetAcceptStates())
{
p.AddEpsilon(s);
}
a.Initial = s;
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
return(a);
}
/// <summary>
/// Reverses the language of the given (non-singleton) automaton while returning the set of
/// new initial states.
/// </summary>
/// <param name="a">The automaton.</param>
/// <returns></returns>
public static HashSet <State> Reverse(Automaton a)
{
// Reverse all edges.
var m = new Dictionary <State, HashSet <Transition> >();
HashSet <State> states = a.GetStates();
HashSet <State> accept = a.GetAcceptStates();
foreach (State r in states)
{
m.Add(r, new HashSet <Transition>());
r.Accept = false;
}
foreach (State r in states)
{
foreach (Transition t in r.Transitions)
{
m[t.To].Add(new Transition(t.Min, t.Max, r));
}
}
foreach (State r in states)
{
r.Transitions = m[r].ToList();
}
// 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.IsDeterministic = false;
return(accept);
}
public static Automaton Concatenate(Automaton a1, Automaton a2)
{
if (a1.IsSingleton && a2.IsSingleton)
{
return(BasicAutomata.MakeString(a1.Singleton + a2.Singleton));
}
if (BasicOperations.IsEmpty(a1) || BasicOperations.IsEmpty(a2))
{
return(BasicAutomata.MakeEmpty());
}
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.IsDeterministic = deterministic;
a1.ClearHashCode();
a1.CheckMinimizeAlways();
return(a1);
}
/// <summary>
/// Reverses the language of the given (non-singleton) automaton while returning the set of
/// new initial states.
/// </summary>
/// <param name="a">The automaton.</param>
/// <returns></returns>
public static HashSet<State> Reverse(Automaton a)
{
// Reverse all edges.
var m = new Dictionary<State, HashSet<Transition>>();
HashSet<State> states = a.GetStates();
HashSet<State> accept = a.GetAcceptStates();
foreach (State r in states)
{
m.Add(r, new HashSet<Transition>());
r.Accept = false;
}
foreach (State r in states)
{
foreach (Transition t in r.Transitions)
{
m[t.To].Add(new Transition(t.Min, t.Max, r));
}
}
foreach (State r in states)
{
r.Transitions = m[r].ToList();
}
// 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.IsDeterministic = false;
return accept;
}
/// <summary>
/// Accepts the Kleene star (zero or more concatenated repetitions) of the language of the
/// given automaton. Never modifies the input automaton language.
/// </summary>
/// <param name="a">The automaton.</param>
/// <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.
/// </returns>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
public static Automaton Repeat(Automaton a)
{
a = a.CloneExpanded();
var s = new State();
s.Accept = true;
s.AddEpsilon(a.Initial);
foreach (State p in a.GetAcceptStates())
{
p.AddEpsilon(s);
}
a.Initial = s;
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
return a;
}
public static Automaton Concatenate(Automaton a1, Automaton a2)
{
if (a1.IsSingleton && a2.IsSingleton)
{
return BasicAutomata.MakeString(a1.Singleton + a2.Singleton);
}
if (BasicOperations.IsEmpty(a1) || BasicOperations.IsEmpty(a2))
{
return BasicAutomata.MakeEmpty();
}
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.IsDeterministic = deterministic;
a1.ClearHashCode();
a1.CheckMinimizeAlways();
return a1;
}
public static Automaton Concatenate(IList <Automaton> l)
{
if (l.Count == 0)
{
return(BasicAutomata.MakeEmptyString());
}
bool allSingleton = l.All(a => a.IsSingleton);
if (allSingleton)
{
var b = new StringBuilder();
foreach (Automaton a in l)
{
b.Append(a.Singleton);
}
return(BasicAutomata.MakeString(b.ToString()));
}
else
{
if (l.Any(a => a.IsEmpty))
{
return(BasicAutomata.MakeEmpty());
}
var ids = new HashSet <int>();
foreach (Automaton a in l)
{
ids.Add(RuntimeHelpers.GetHashCode(a));
}
bool hasAliases = ids.Count != l.Count;
Automaton b = l[0];
b = hasAliases ? b.CloneExpanded() : b.CloneExpandedIfRequired();
var ac = b.GetAcceptStates();
bool first = true;
foreach (Automaton a in l)
{
if (first)
{
first = false;
}
else
{
if (a.IsEmptyString())
{
continue;
}
Automaton aa = a;
aa = hasAliases ? aa.CloneExpanded() : aa.CloneExpandedIfRequired();
HashSet <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.IsDeterministic = false;
b.ClearHashCode();
b.CheckMinimizeAlways();
return(b);
}
}
