/// <summary>
/// Create Deterministic Finite Automaton by lazy form of subset construction (Rabin and Scott, )
/// </summary>
/// <returns>Deterministic Finite Automaton created by lazy form of subset construction</returns>
public LrItemsDfa <TTokenKind> ToDfa()
{
// The subset construction is an example of a fixed-point computation, where an application of a
// monotone function to some collection of sets drawn from a domain whose structure is known is
// performed iteratively. The computation will terminate when an iteration step produces a state
// where further iteration produces the same answer — a “fixed point” in the space of successive
// iterates.
//
// For the subset construction, the domain is the power set of all possible subsets of the NFA states.
// The while loop adds elements (subsets) to Q; it cannot remove an element from Q. We can view
// the while loop as a monotone increasing function f, which means that for a set x, f(x) ≥ x. (The
// comparison operator ≥ is ⊇.) Since Q can have at most 2^N distinct elements, the while loop can iterate
// at most 2^N times. It may, of course, reach a fixed point and halt more quickly than that.
var newStartState = EpsilonClose(StartState.AsSingletonEnumerable());
var newAcceptStates = new HashSet <ProductionItemSet <TTokenKind> >();
var newTransitions = new List <Transition <Symbol, ProductionItemSet <TTokenKind> > >();
var newStates = new InsertionOrderedSet <ProductionItemSet <TTokenKind> > {
newStartState
};
// Lazy form of Subset Construction where only reachable nodes
// are added to the following work list of marked subsets
var markedVisitedStates = new Queue <ProductionItemSet <TTokenKind> >(); // work list that preserves insertion order
markedVisitedStates.Enqueue(newStartState);
while (markedVisitedStates.Count != 0)
{
// subset S
ProductionItemSet <TTokenKind> subsetSourceState = markedVisitedStates.Dequeue();
if (subsetSourceState.Overlaps(GetAcceptStates()))
{
newAcceptStates.Add(subsetSourceState);
}
// For all non-epsilon labels
foreach (var label in GetAlphabet())
{
// subset T
var subsetTargetState = new Set <ProductionItem <TTokenKind> >();
// kernel items: For all s in S, add all non-epsilon transitions (s, label) → t to T
foreach (ProductionItem <TTokenKind> s in subsetSourceState)
{
subsetTargetState.AddRange(Delta(Transition.FromPair(s, label)));
}
// Ignore empty subset (implicit transition to dead state in this case)
if (subsetTargetState.Count == 0)
{
continue;
}
// Closure Items: Epsilon-close all T such that (S, label) → T
var closure = EpsilonClose(subsetTargetState);
if (!newStates.Contains(closure))
{
newStates.Add(closure);
markedVisitedStates.Enqueue(closure);
}
// Add (S, label) → T transition
newTransitions.Add(Transition.Move(subsetSourceState, label, closure));
}
}
return(new LrItemsDfa <TTokenKind>(newStates, GetAlphabet(), newTransitions, newStartState, newAcceptStates));
}