public static Sfsa Concat(this Sfsa first, Sfsa second)
{
var firstFinalStates = first.Final;
second = Remap(second, first.States);
var secondInitialStates = second.Initial;
var initialStates = first.Initial.Intersect(first.Final).Any()
? first.Initial.Union(second.Initial)
: first.Initial;
var transitions = first.Transitions.Union(second.Transitions).ToList();
foreach (var tr in first.Transitions.Where(t => first.Final.Contains(t.To)))
{
foreach (var state in second.Initial)
{
transitions.Add((tr.From, tr.Label, state));
}
}
return(new Sfsa(
states: first.States.Union(second.States),
initialStates,
second.Final,
transitions));
}
// Kleene star operation on a finite automaton
public static Sfsa Star(this Sfsa automaton)
{
var initial = NewState(automaton.States);
var initialStates = new int[] { initial };
var newTransitions = new List <(int, Range, int)>();
foreach (var state in automaton.Initial)
{
newTransitions.Add((initial, default, state));
public static Sfsa Union(this Sfsa first, Sfsa second)
{
second = Remap(second, first.States);
return(new Sfsa(
states: first.States.Union(second.States),
initial: first.Initial.Union(second.Initial),
final: first.Final.Union(second.Final),
transitions: first.Transitions.Union(second.Transitions)));
}
// Clones the finite automaton by renaming the states
static Sfsa Remap(this Sfsa automaton, IReadOnlyCollection <int> states)
{
var k = states.Count;
return(new Sfsa(
automaton.States.Select(s => s + k),
automaton.Initial.Select(s => s + k),
automaton.Final.Select(s => s + k),
automaton.Transitions.Select(t => (t.From + k, t.Label, t.To + k))));
}
public static Sfsa Concat(this Sfsa fsa, params Sfsa[] automata) => automata.Aggregate(fsa, Concat);
