/// <summary>
/// Returns an automaton that accepts the union of the languages of the given automata.
/// </summary>
/// <param name="automatons">The l.</param>
/// <returns>
/// An automaton that accepts the union of the languages of the given automata.
/// </returns>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
public static Automaton Union(IList <Automaton> automatons)
{
var ids = new HashSet <int>();
foreach (Automaton a in automatons)
{
ids.Add(RuntimeHelpers.GetHashCode(a));
}
bool hasAliases = ids.Count != automatons.Count;
var s = new State();
foreach (Automaton b in automatons)
{
if (b.IsEmpty)
{
continue;
}
Automaton bb = b;
bb = hasAliases ? bb.CloneExpanded() : bb.CloneExpandedIfRequired();
s.AddEpsilon(bb.Initial);
}
var automaton = new Automaton();
automaton.Initial = s;
automaton.IsDeterministic = false;
automaton.ClearHashCode();
automaton.CheckMinimizeAlways();
return(automaton);
}
/// <summary>
/// Returns a new automaton that accepts strings representing decimal non-negative integers in
/// the given interval.
/// </summary>
/// <param name="min">The minimum value of interval.</param>
/// <param name="max">The maximum value of inverval (both end points are included in the
/// interval).</param>
/// <param name="digits">If f >0, use fixed number of digits (strings must be prefixed by 0's
/// to obtain the right length) otherwise, the number of digits is not fixed.</param>
/// <returns>A new automaton that accepts strings representing decimal non-negative integers
/// in the given interval.</returns>
public static Automaton MakeInterval(int min, int max, int digits)
{
if (min > max)
{
throw new ArgumentException("min must not be greater than max.");
}
var a = new Automaton();
string x = Convert.ToString(min, CultureInfo.CurrentCulture);
string y = Convert.ToString(max, CultureInfo.CurrentCulture);
if ((digits > 0 && y.Length > digits))
{
throw new ArgumentException($"Fixed length output specified ({digits}), but will not fit max ({y.Length}).");
}
int d = digits > 0 ? digits : y.Length;
var bx = new StringBuilder();
for (int i = x.Length; i < d; i++)
{
bx.Append('0');
}
bx.Append(x);
x = bx.ToString();
var by = new StringBuilder();
for (int i = y.Length; i < d; i++)
{
by.Append('0');
}
by.Append(y);
y = by.ToString();
ICollection <State> initials = new List <State>();
a.Initial = BasicAutomata.Between(x, y, 0, initials, digits <= 0);
if (digits <= 0)
{
List <StatePair> pairs = (from p in initials
where a.Initial != p
select new StatePair(a.Initial, p)).ToList();
a.AddEpsilons(pairs);
a.Initial.AddTransition(new Transition('0', a.Initial));
a.IsDeterministic = false;
}
else
{
a.IsDeterministic = true;
}
a.CheckMinimizeAlways();
return(a);
}
/// <summary>
/// Returns an automaton that accepts the union of the empty string and the language of the
/// given automaton.
/// </summary>
/// <param name="a">The automaton.</param>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
/// <returns>An automaton that accepts the union of the empty string and the language of the
/// given automaton.</returns>
public static Automaton Optional(Automaton a)
{
a = a.CloneExpandedIfRequired();
var s = new State();
s.AddEpsilon(a.Initial);
s.Accept = true;
a.Initial = s;
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
return(a);
}
/// <summary>
/// Returns a new automaton that accepts strings representing decimal non-negative integers in
/// the given interval.
/// </summary>
/// <param name="min">The minimum value of interval.</param>
/// <param name="max">The maximum value of inverval (both end points are included in the
/// interval).</param>
/// <param name="digits">If f >0, use fixed number of digits (strings must be prefixed by 0's
/// to obtain the right length) otherwise, the number of digits is not fixed.</param>
/// <returns>A new automaton that accepts strings representing decimal non-negative integers
/// in the given interval.</returns>
public static Automaton MakeInterval(int min, int max, int digits)
{
var a = new Automaton();
string x = Convert.ToString(min);
string y = Convert.ToString(max);
if (min > max || (digits > 0 && y.Length > digits))
{
throw new ArgumentException();
}
int d = digits > 0 ? digits : y.Length;
var bx = new StringBuilder();
for (int i = x.Length; i < d; i++)
{
bx.Append('0');
}
bx.Append(x);
x = bx.ToString();
var by = new StringBuilder();
for (int i = y.Length; i < d; i++)
{
by.Append('0');
}
by.Append(y);
y = by.ToString();
ICollection <State> initials = new List <State>();
a.Initial = BasicAutomata.Between(x, y, 0, initials, digits <= 0);
if (digits <= 0)
{
List <StatePair> pairs = (from p in initials
where a.Initial != p
select new StatePair(a.Initial, p)).ToList();
a.AddEpsilons(pairs);
a.Initial.AddTransition(new Transition('0', a.Initial));
a.IsDeterministic = false;
}
else
{
a.IsDeterministic = true;
}
a.CheckMinimizeAlways();
return(a);
}
/// <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);
}
/// <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>
/// Returns an automaton that accepts the union of the empty string and the language of the
/// given automaton.
/// </summary>
/// <param name="a">The automaton.</param>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
/// <returns>An automaton that accepts the union of the empty string and the language of the
/// given automaton.</returns>
public static Automaton Optional(Automaton a)
{
a = a.CloneExpandedIfRequired();
var s = new State();
s.AddEpsilon(a.Initial);
s.Accept = true;
a.Initial = s;
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
return a;
}
/// <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">The automaton.</param>
/// <param name="pairs">A 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();
var forward = new Dictionary<State, HashSet<State>>();
var back = new Dictionary<State, HashSet<State>>();
foreach (StatePair p in pairs)
{
HashSet<State> to = forward[p.FirstState];
if (to == null)
{
to = new HashSet<State>();
forward.Add(p.FirstState, to);
}
to.Add(p.SecondState);
HashSet<State> from = back[p.SecondState];
if (from == null)
{
from = new HashSet<State>();
back.Add(p.SecondState, from);
}
from.Add(p.FirstState);
}
var worklist = new LinkedList<StatePair>(pairs);
var workset = new HashSet<StatePair>(pairs);
while (worklist.Count != 0)
{
StatePair p = worklist.RemoveAndReturnFirst();
workset.Remove(p);
HashSet<State> to = forward[p.SecondState];
HashSet<State> from = back[p.FirstState];
if (to != null)
{
foreach (State s in to)
{
var pp = new StatePair(p.FirstState, s);
if (!pairs.Contains(pp))
{
pairs.Add(pp);
forward[p.FirstState].Add(s);
back[s].Add(p.FirstState);
worklist.AddLast(pp);
workset.Add(pp);
if (from != null)
{
foreach (State q in from)
{
var qq = new StatePair(q, p.FirstState);
if (!workset.Contains(qq))
{
worklist.AddLast(qq);
workset.Add(qq);
}
}
}
}
}
}
}
// Add transitions.
foreach (StatePair p in pairs)
{
p.FirstState.AddEpsilon(p.SecondState);
}
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
}
/// <summary>
/// Returns an automaton that accepts the intersection of the languages of the given automata.
/// Never modifies the input automata languages.
/// </summary>
/// <param name="a1">The a1.</param>
/// <param name="a2">The a2.</param>
/// <returns></returns>
public static Automaton Intersection(Automaton a1, Automaton a2)
{
if (a1.IsSingleton)
{
if (a2.Run(a1.Singleton))
{
return a1.CloneIfRequired();
}
return BasicAutomata.MakeEmpty();
}
if (a2.IsSingleton)
{
if (a1.Run(a2.Singleton))
{
return a2.CloneIfRequired();
}
return BasicAutomata.MakeEmpty();
}
if (a1 == a2)
{
return a1.CloneIfRequired();
}
Transition[][] transitions1 = Automaton.GetSortedTransitions(a1.GetStates());
Transition[][] transitions2 = Automaton.GetSortedTransitions(a2.GetStates());
var c = new Automaton();
var worklist = new LinkedList<StatePair>();
var newstates = new Dictionary<StatePair, StatePair>();
var p = new StatePair(c.Initial, a1.Initial, a2.Initial);
worklist.AddLast(p);
newstates.Add(p, p);
while (worklist.Count > 0)
{
p = worklist.RemoveAndReturnFirst();
p.S.Accept = p.FirstState.Accept && p.SecondState.Accept;
Transition[] t1 = transitions1[p.FirstState.Number];
Transition[] t2 = transitions2[p.SecondState.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)
{
var 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.Add(q, q);
r = q;
}
char min = t1[n1].Min > t2[n2].Min ? t1[n1].Min : t2[n2].Min;
char max = t1[n1].Max < t2[n2].Max ? t1[n1].Max : t2[n2].Max;
p.S.Transitions.Add(new Transition(min, max, r.S));
}
}
}
}
c.IsDeterministic = a1.IsDeterministic && a2.IsDeterministic;
c.RemoveDeadTransitions();
c.CheckMinimizeAlways();
return c;
}
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>
/// Returns an automaton that accepts the union of the languages of the given automata.
/// </summary>
/// <param name="automatons">The l.</param>
/// <returns>
/// An automaton that accepts the union of the languages of the given automata.
/// </returns>
/// <remarks>
/// Complexity: linear in number of states.
/// </remarks>
public static Automaton Union(IList<Automaton> automatons)
{
var ids = new HashSet<int>();
foreach (Automaton a in automatons)
{
ids.Add(RuntimeHelpers.GetHashCode(a));
}
bool hasAliases = ids.Count != automatons.Count;
var s = new State();
foreach (Automaton b in automatons)
{
if (b.IsEmpty)
{
continue;
}
Automaton bb = b;
bb = hasAliases ? bb.CloneExpanded() : bb.CloneExpandedIfRequired();
s.AddEpsilon(bb.Initial);
}
var automaton = new Automaton();
automaton.Initial = s;
automaton.IsDeterministic = false;
automaton.ClearHashCode();
automaton.CheckMinimizeAlways();
return automaton;
}
/// <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">The automaton.</param>
/// <param name="pairs">A 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();
var forward = new Dictionary <State, HashSet <State> >();
var back = new Dictionary <State, HashSet <State> >();
foreach (StatePair p in pairs)
{
HashSet <State> to = forward[p.FirstState];
if (to == null)
{
to = new HashSet <State>();
forward.Add(p.FirstState, to);
}
to.Add(p.SecondState);
HashSet <State> from = back[p.SecondState];
if (from == null)
{
from = new HashSet <State>();
back.Add(p.SecondState, from);
}
from.Add(p.FirstState);
}
var worklist = new LinkedList <StatePair>(pairs);
var workset = new HashSet <StatePair>(pairs);
while (worklist.Count != 0)
{
StatePair p = worklist.RemoveAndReturnFirst();
workset.Remove(p);
HashSet <State> to = forward[p.SecondState];
HashSet <State> from = back[p.FirstState];
if (to != null)
{
foreach (State s in to)
{
var pp = new StatePair(p.FirstState, s);
if (!pairs.Contains(pp))
{
pairs.Add(pp);
forward[p.FirstState].Add(s);
back[s].Add(p.FirstState);
worklist.AddLast(pp);
workset.Add(pp);
if (from != null)
{
foreach (State q in from)
{
var qq = new StatePair(q, p.FirstState);
if (!workset.Contains(qq))
{
worklist.AddLast(qq);
workset.Add(qq);
}
}
}
}
}
}
}
// Add transitions.
foreach (StatePair p in pairs)
{
p.FirstState.AddEpsilon(p.SecondState);
}
a.IsDeterministic = false;
a.ClearHashCode();
a.CheckMinimizeAlways();
}
/// <summary>
/// Returns an automaton that accepts the intersection of the languages of the given automata.
/// Never modifies the input automata languages.
/// </summary>
/// <param name="a1">The a1.</param>
/// <param name="a2">The a2.</param>
/// <returns></returns>
public static Automaton Intersection(Automaton a1, Automaton a2)
{
if (a1.IsSingleton)
{
if (a2.Run(a1.Singleton))
{
return(a1.CloneIfRequired());
}
return(BasicAutomata.MakeEmpty());
}
if (a2.IsSingleton)
{
if (a1.Run(a2.Singleton))
{
return(a2.CloneIfRequired());
}
return(BasicAutomata.MakeEmpty());
}
if (a1 == a2)
{
return(a1.CloneIfRequired());
}
Transition[][] transitions1 = Automaton.GetSortedTransitions(a1.GetStates());
Transition[][] transitions2 = Automaton.GetSortedTransitions(a2.GetStates());
var c = new Automaton();
var worklist = new LinkedList <StatePair>();
var newstates = new Dictionary <StatePair, StatePair>();
var p = new StatePair(c.Initial, a1.Initial, a2.Initial);
worklist.AddLast(p);
newstates.Add(p, p);
while (worklist.Count > 0)
{
p = worklist.RemoveAndReturnFirst();
p.S.Accept = p.FirstState.Accept && p.SecondState.Accept;
Transition[] t1 = transitions1[p.FirstState.Number];
Transition[] t2 = transitions2[p.SecondState.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)
{
var 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.Add(q, q);
r = q;
}
char min = t1[n1].Min > t2[n2].Min ? t1[n1].Min : t2[n2].Min;
char max = t1[n1].Max < t2[n2].Max ? t1[n1].Max : t2[n2].Max;
p.S.Transitions.Add(new Transition(min, max, r.S));
}
}
}
}
c.IsDeterministic = a1.IsDeterministic && a2.IsDeterministic;
c.RemoveDeadTransitions();
c.CheckMinimizeAlways();
return(c);
}
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);
}
}
/// <summary>
/// Returns a new automaton that accepts strings representing decimal non-negative integers in
/// the given interval.
/// </summary>
/// <param name="min">The minimum value of interval.</param>
/// <param name="max">The maximum value of inverval (both end points are included in the
/// interval).</param>
/// <param name="digits">If f >0, use fixed number of digits (strings must be prefixed by 0's
/// to obtain the right length) otherwise, the number of digits is not fixed.</param>
/// <returns>A new automaton that accepts strings representing decimal non-negative integers
/// in the given interval.</returns>
public static Automaton MakeInterval(int min, int max, int digits)
{
var a = new Automaton();
string x = Convert.ToString(min);
string y = Convert.ToString(max);
if (min > max || (digits > 0 && y.Length > digits))
{
throw new ArgumentException();
}
int d = digits > 0 ? digits : y.Length;
var bx = new StringBuilder();
for (int i = x.Length; i < d; i++)
{
bx.Append('0');
}
bx.Append(x);
x = bx.ToString();
var by = new StringBuilder();
for (int i = y.Length; i < d; i++)
{
by.Append('0');
}
by.Append(y);
y = by.ToString();
ICollection<State> initials = new List<State>();
a.Initial = BasicAutomata.Between(x, y, 0, initials, digits <= 0);
if (digits <= 0)
{
List<StatePair> pairs = (from p in initials
where a.Initial != p
select new StatePair(a.Initial, p)).ToList();
a.AddEpsilons(pairs);
a.Initial.AddTransition(new Transition('0', a.Initial));
a.IsDeterministic = false;
}
else
{
a.IsDeterministic = true;
}
a.CheckMinimizeAlways();
return a;
}
