/// <summary>
/// Returns the set of all states that can be reached by following epsilon transitions only
/// </summary>
/// <param name="nfa"></param>
/// <param name="group"></param>
/// <returns></returns>
public Set <TState> EpsilonClosure(INFA <TState, TInput, TTransition> nfa, IEnumerable <TState> group)
{
var queue = new Queue <TState>(group);
var closure = new Set <TState>();
while (queue.Count != 0)
{
var state = queue.Dequeue();
closure.Add(state);
// Targets reachable from the current node not already added to the closure
var epsilonTargets =
nfa.FromSource(state)
.Where(t => t.Input.Equals(nfa.Epsilon))
.Where(t => !closure.Contains(t.Target))
.Select(t => t.Target);
foreach (var target in epsilonTargets)
{
queue.Enqueue(target);
}
}
return(closure);
}
/// <summary>
/// Generates and returns the equivalent <see cref="IDFA{TState, TInput, TTransition}"/>
/// from the supplied <see cref="INFA{TState, TInput, TTransition}"/>
/// </summary>
/// <param name="nfa"></param>
/// <returns></returns>
public IDFA <TState, TInput, TTransition> DFAFromNFA(INFA <TState, TInput, TTransition> nfa)
{
var partial = RemoveDeadStates(EquivalenceMinimization(DFA(nfa)));
return(new DFA <TState, TInput, TTransition>(
partial.Initial,
partial.Terminals,
partial.Transitions
));
}
/// <summary>
/// Transforms an <see cref="INFA{TState, TInput, TTransition}"/> to a
/// <see cref="IDFA{TState, TInput, TTransition}"/> by removing all epsilon
/// transitions from an NFA by compositing states and transitions under
/// epsilon closures
/// </summary>
/// <param name="nfa"></param>
/// <returns></returns>
public PartialDFA DFA(
INFA <TState, TInput, TTransition> nfa)
{
var first = EpsilonClosure(nfa, Set <TState> .Of(nfa.Initial));
var groupTransitions = new List <TGroupTransition>();
var terminalGroups = new List <Set <TState> >();
// Create work queue of groups to process
var unmarkedGroups = new Queue <Set <TState> >();
unmarkedGroups.Enqueue(first);
var markedGroups = new Set <Set <TState> >();
while (unmarkedGroups.Any())
{
var group = unmarkedGroups.Dequeue();
markedGroups.Add(group);
if (group.Contains(nfa.Terminal))
{
terminalGroups.Add(group);
}
// Find new epsilon closed group for each possible input
foreach (var input in nfa.Inputs.Where(i => !i.Equals(nfa.Epsilon)))
{
var closure = EpsilonClosure(nfa, nfa.Move(group, input));
if (!closure.Any())
{
continue;
}
// Add unseen groups to unmarked groups
if (!unmarkedGroups.Contains(closure) &&
!markedGroups.Contains(closure))
{
unmarkedGroups.Enqueue(closure);
}
// Add the newly formed transition
groupTransitions.Add(GroupTransition(group, input, closure));
}
}
return(Reduce(
first,
terminalGroups,
groupTransitions
));
}