/// <summary>
/// Transform the specified Non-Deterministic Buchi Automata into a Deterministic Rabin Automata.
/// </summary>
/// <param name="ba">Buchi Automata.</param>
public static RabinAutomaton<AutomatonNode> Determinize(this BuchiAutomaton<AutomatonNode> ba)
{
var Transitions = new Dictionary<SafraTree, List<SafraTransition>> ();
// For more details about the algorithm, check "Determinization of Büchi-Automata" by Markus Roggenbach
var initial = new SafraTree (new [] { ba.InitialNode }, ba);
var pending = new Stack<SafraTree> (new [] { initial });
var visited = new HashSet<SafraTree> ();
while (pending.Count > 0) {
var source = pending.Pop ();
visited.Add (source);
foreach (var a in ba.GetOutDecorations (source.MacroState)) {
var target = source.Clone ();
target.RemoveAllMarks (); // Step 1
target.Create (); // Step 2
target.Update (a.LiteralSet); // Step 3
target.HorizontalMerge (); // Step 4
target.RemoveEmpty (); // Step 5
if (target.MacroState.Count > 0) {
target.VerticalMerge (); // Step 6
if (!Transitions.ContainsKey (source))
Transitions.Add (source, new List<SafraTransition> ());
Transitions[source].Add (new SafraTransition (a.LiteralSet, target));
if (!Transitions.ContainsKey (target) & !pending.Contains (target))
pending.Push (target);
}
}
}
var rabin = new RabinAutomaton<AutomatonNode> (new AutomatonNodeFactory ());
var mapping = new Dictionary<SafraTree, AutomatonNode> ();
foreach (var t in Transitions.Keys) {
var n = rabin.AddNode ();
mapping.Add (t, n);
}
rabin.SetInitialNode (mapping [initial]);
foreach (var t in Transitions) {
foreach (var e in t.Value) {
rabin.AddTransition (mapping [t.Key], mapping [e.Target], new LiteralSetDecoration (e.Labels));
}
}
foreach (int k in Transitions.Keys.Select(t => t.Id).Distinct ()) {
var r1 = Transitions.Keys.Where (x => !x.ContainsIdentifier (k)).Select (x => mapping[x]);
var r2 = Transitions.Keys.Where (x => x.ContainsMarkedNode (k)).Select (x => mapping[x]);
rabin.AddToAcceptance (r1, r2);
}
return rabin;
}
static string PrintTree(SafraTree t, int indent = 0)
{
return new String ('-', indent)
+ t.Id
+ " - "
+ string.Join (",", t.MacroState.Select (x => x.Name))
+ " - "
+ (t.Mark ? "!" : "")
+ "\n"
+ string.Join ("\n", t.Children.Select (x => PrintTree (x, indent + 1)));
}
/// <summary>
/// Creates a new child if there is a set in the macro state that is accepting in the Buchi Automata.
/// The procedure is recursively applied on children.
/// </summary>
public void Create()
{
var children = Children.ToList ();
var inter = ((BuchiAcceptance<AutomatonNode>) ba.AcceptanceCondition).GetAcceptingNodes (MacroState);
if (inter.Any ()) {
var newNode = new SafraTree (inter, ba);
Children.Add (newNode);
}
foreach (var c in children) {
c.Create ();
}
}
/// <summary>
/// Initializes a new instance of the
/// <see cref="LtlSharp.Translators.SafraDeterminization+SafraTransition"/> class
/// with the specified label and target safra tree.
/// </summary>
/// <param name="labels">Labels.</param>
/// <param name="target">Target.</param>
public SafraTransition(LiteralSet labels, SafraTree target)
{
this.Labels = labels;
this.Target = target;
}
