public static NFA AnyOf(NFA left, NFA right)
{
var result = new NFA();
result.AddState(0, false);
result.AddTransition(0, result.Add(left), Epsilon);
result.AddTransition(0, result.Add(right), Epsilon);
return(result);
}
private int Add(NFA left)
{
int stateOffset = NewState();
foreach (var s in left.states)
{
AddState(s + stateOffset, left.final.Contains(s));
}
foreach (var t in left.transitions)
{
AddTransition(t.Item1 + stateOffset, t.Item2 + stateOffset, t.Item3);
}
return(stateOffset);
}
public static NFA Concat(NFA left, NFA right)
{
var result = new NFA();
result.Add(left);
var leftFinals = result.final.ToArray();
result.final.Clear();
int rightInitial = result.Add(right);
foreach (var final in leftFinals)
{
result.AddTransition(final, rightInitial, Epsilon);
}
return(result);
}
public static NFA Star(NFA input)
{
var result = new NFA();
var newFinal = result.NewState();
result.AddState(newFinal, true);
var start = result.Add(input);
var finals = result.final.Where(h => h != newFinal).ToArray();
foreach (var final in finals)
{
result.AddTransition(final, start, Epsilon);
}
result.AddTransition(newFinal, start, Epsilon);
return(result);
}
public NFA Determinize()
{
NFA target = new NFA();
Stack <Tuple <int, HashSet <int> > > frontier = new Stack <Tuple <int, HashSet <int> > >();
Dictionary <HashSet <int>, int> seen = new Dictionary <HashSet <int>, int>(new SetStateComparer());
int set_key = 0;
HashSet <int> set_initial = new HashSet <int>();
set_initial.Add(0);
EpsilonClosure(set_initial);
target.AddState(set_key, ContainsFinalState(set_initial));
frontier.Push(new Tuple <int, HashSet <int> >(set_key, set_initial));
seen[set_initial] = set_key;
while (frontier.Count > 0)
{
var current = frontier.Pop();
var current_key = current.Item1;
var current_set = current.Item2;
bool hasA = false, hasB = false;
foreach (var st in current_set)
{
foreach (var t in FindTransitions(st))
{
if (t.Item3 == Epsilon)
{
continue;
}
else if (t.Item3 == 'a')
{
hasA = true;
}
else if (t.Item3 == 'b')
{
hasB = true;
}
if (hasA && hasB)
{
break;
}
}
if (hasA && hasB)
{
break;
}
}
var inputs = "ab";
if (!(hasA & hasB))
{
inputs = hasA ? "a" : "b";
}
foreach (var i in inputs)
{
HashSet <int> new_state = new HashSet <int>();
HashSet <char> new_transitions = new HashSet <char>();
foreach (var st in current_set)
{
foreach (var t in FindTransitions(st).Where(j => j.Item3 == i))
{
new_transitions.Add(t.Item3);
new_state.Add(t.Item2);
}
}
EpsilonClosure(new_state);
int seen_state_key;
if (!seen.TryGetValue(new_state, out seen_state_key))
{
set_key++;
target.AddState(set_key, ContainsFinalState(new_state));
foreach (var t in new_transitions)
{
target.AddTransition(current_key, set_key, t);
}
frontier.Push(new Tuple <int, HashSet <int> >(set_key, new_state));
seen[new_state] = set_key;
}
else
{
foreach (var t in new_transitions)
{
target.AddTransition(current_key, seen_state_key, t);
}
}
}
}
return(target);
}
public NFA Parse(string input)
{
//Shunting-Yard algorithm
Stack <char> s = new Stack <char>();
List <char> q = new List <char>();
var c = input.GetEnumerator();
char prev = '\0';
while (c.MoveNext())
{
switch (c.Current)
{
case 'a':
case 'b':
q.Add(c.Current);
if (prev == 'a' || prev == 'b' || prev == ')')
{
s.Push('-');
}
break;
case '(':
if (prev == 'a' || prev == 'b' || prev == ')')
{
s.Push('-');
}
s.Push(c.Current);
break;
case '*':
case '|':
s.Push(c.Current);
break;
case ')':
while (s.Count > 0 && s.Peek() != '(')
{
q.Add(s.Pop());
}
s.Pop();
break;
}
prev = c.Current;
}
Stack <NFA> calc = new Stack <NFA>();
foreach (var i in q)
{
if (i == '*')
{
calc.Push(NFA.Star(calc.Pop()));
}
else if (i == '-')
{
var right = calc.Pop();
var left = calc.Pop();
calc.Push(NFA.Concat(left, right));
}
else if (i == '|')
{
var right = calc.Pop();
var left = calc.Pop();
calc.Push(NFA.AnyOf(left, right));
}
else
{
NFA nfa = new NFA();
nfa.AddState(0, false);
nfa.AddState(1, true);
nfa.AddTransition(0, 1, i);
calc.Push(nfa);
}
}
return(calc.Pop());
}
