public static FA Single(Integers terminal)
{
var start = new State();
var end = new State();
start.Add(terminal, end);
return(FA.From(start, end));
}
public static FA None()
{
var start = new State();
var illegal = new State();
start.Add(Integers.Any, illegal);
illegal.Add(Integers.Any, illegal);
return(FA.From(start, start));
}
public static FA Concat(FA fa, FA other)
{
var first = fa.ToNfa(true);
Debug.Assert(first.Final != null);
other = other.ToNfa(true);
Debug.Assert(other.Final != null);
first.Final.Add(other.Start);
return(FA.From(first.Start, other.Final));
}
public static FA From(string sequence)
{
Debug.Assert(!string.IsNullOrEmpty(sequence));
var start = new State();
var current = start;
var next = (State?)null;
foreach (var ch in sequence)
{
next = new State();
current.Add(Integers.From(ch), next);
current = next;
}
Debug.Assert(next != null);
return(FA.From(start, next));
}
public static FA Or(FA fa, FA other)
{
var first = fa.ToNfa(true);
Debug.Assert(first.Final != null);
var second = other.ToNfa(true);
Debug.Assert(second.Final != null);
var newEnd = new State();
first.Start.Add(second.Start);
first.Final.Add(newEnd);
second.Final.Add(newEnd);
return(FA.From(first.Start, newEnd));
}
private FA MergeStates(FA dfa)
{
//
// https://en.wikipedia.org/wiki/DFA_minimization
// Hopcroft's algorithm
//
#if true
var nons = new StateSet(dfa.Nons.ToList());
var all = dfa.States.ToList();
var partitions = new List <StateSet> {
nons
};
var working = new List <StateSet> {
nons
};
var fgroups = from state in dfa.Finals group state by state.Payload;
foreach (var fgroup in fgroups)
{
partitions.Add(new StateSet(fgroup));
}
#else
var finals = new StateSet(dfa.Finals.ToList());
var nons = new StateSet(dfa.Nons.ToList());
var all = dfa.States.ToList();
var partitions = new List <StateSet> {
finals, nons
};
var working = new List <StateSet> {
finals
};
#endif
var terminals = new HashSet <Integers>(all.SelectMany(state => state.Transitions).Select(transition => transition.Set));
while (working.Count > 0)
{
var a = working[0];
working.RemoveAt(0);
foreach (var terminal in terminals)
{
var x = new StateSet();
foreach (var state in all)
{
foreach (var transition in state.Transitions)
{
if (transition.Set.Overlaps(terminal))
{
if (a.Contains(transition.Target))
{
x.Add(state);
break;
}
}
}
}
var i = 0;
while (i < partitions.Count)
{
var y = partitions[i];
var x_intersect_y = x.IntersectWith(y);
var y_without_x = y.ExceptWith(x);
if (x_intersect_y.IsEmpty || y_without_x.IsEmpty)
{
i += 1;
continue;
}
partitions[i] = x_intersect_y;
i += 1;
partitions.Insert(i, y_without_x);
i += 1;
var j = 0;
while (j < working.Count)
{
if (working[j] == y)
{
working.RemoveAt(j);
working.Add(x_intersect_y);
working.Add(y_without_x);
break;
}
j += 1;
}
if (j == working.Count)
{
// ReSharper disable once ConvertIfStatementToConditionalTernaryExpression
if (x_intersect_y.Count <= y_without_x.Count)
{
working.Add(x_intersect_y);
}
else
{
working.Add(y_without_x);
}
}
}
}
}
foreach (var partition in partitions)
{
if (partition.Count >= 1)
{
#if true
var groups = from s in partition group s by s.Payload;
foreach (var group in groups)
{
List <State> dfaStates = group.ToList();
var premium = dfaStates.First();
var remove = dfaStates.Skip(1).ToList();
foreach (var state in all)
{
foreach (var transition in state.Transitions)
{
if (remove.Contains(transition.Target))
{
transition.Retarget(premium);
}
}
}
EnsureDistinctTransitions(premium);
}
#else
List <State> dfaStates = partition.ToList();
var premium = dfaStates.First();
var remove = dfaStates.Skip(1).ToList();
foreach (var state in all)
{
foreach (var transition in state.Transitions)
{
if (remove.Contains(transition.Target))
{
transition.Retarget(premium);
}
}
}
EnsureDistinctTransitions(premium);
#endif
}
}
var result = FA.From(dfa.Start);
EnsureDfa(result);
return(result);
}