public double Satisfy (State s, Finally @finally)
{
// Search states such that enclosed in finally is true
var validStates = States.Where (x => Satisfy(x, @finally.Enclosed) > 0);
if (validStates.Contains (s))
return 1;
else if (validStates.Count () == 0)
return 0;
Console.WriteLine ("---------- [States satisfying enclosed]");
Console.WriteLine (string.Join (", ", validStates.Select (x => x.Identifier)));
Console.WriteLine ("----------");
var smToValidStates = new MarkovChain ();
foreach (var state in validStates) {
DFS (validStates, smToValidStates);
}
Console.WriteLine ("---------- [States in S tilde]");
Console.WriteLine (string.Join (", ", smToValidStates.States.Select (x => x.Identifier)));
Console.WriteLine ("----------");
var table = smToValidStates.BuildConversionTable ();
var transitions = smToValidStates.GetTransitionMatrix(table);
/*
Console.WriteLine ("---------- [Conversion Table]");
Console.WriteLine (string.Join ("\n", table.Select (x => x.Key + ":" + x.Value)));
Console.WriteLine ("----------");
Console.WriteLine ("---------- [Transitions]");
Console.WriteLine (transitions);
Console.WriteLine ("----------");
*/
// Build the transition matrix for this sub state-machine
var system = new DiagonalMatrix (transitions.RowCount, transitions.ColumnCount, 1)
- transitions;
/*
Console.WriteLine ("---------- [System]");
Console.WriteLine (system);
Console.WriteLine ("----------");
*/
var vector = new DenseVector (
smToValidStates.States.Select (x =>
Transitions.Where (y => y.From.Equals (x))
.Where (y => validStates.Contains (y.To))
.Select (y => y.Probability).Sum ()
).ToArray ()
);
/*
Console.WriteLine ("---------- [Vector]");
Console.WriteLine (vector);
Console.WriteLine ("----------");
*/
var result = system.LU ().Solve (vector);
/*
Console.WriteLine ("---------- [Result]");
Console.WriteLine (result);
Console.WriteLine ("----------");
*/
return table.ContainsKey (s.Identifier) ? result[table[s.Identifier]] : 0;
}
public double Satisfy (State currentState, Until until)
{
if (caching.ContainsKey (until)) {
return caching[until][currentState];
}
caching[until] = new Dictionary<State, double> ();
var B = until.Left;
var C = until.Right;
// Compute SO
var s0 = States.Except (ComputeNotS0 (States.Where (s => Satisfy (s, B) == 1), C));
Console.WriteLine ("S0 : " + string.Join (",", s0.Select (s => s.Identifier)));
foreach (var s in s0)
caching[until].Add (s, 0);
// Compute S1
var s1 = ComputeS1 (B, C);
Console.WriteLine ("S1 : " + string.Join (",", s1.Select (s => s.Identifier)));
foreach (var s in s1)
caching[until].Add (s, 1);
// Compute S?
var spending = States.Except (s0.Union(s1));
Console.WriteLine ("S? : " + string.Join (",", spending.Select (s => s.Identifier)));
if (spending.Count() > 0) {
// Build a SM with only states from S?
var sm = new MarkovChain ();
foreach (var s in spending) {
sm.Add (s);
foreach (var t in spending) {
var transition = Transitions.Where (trans => trans.From.Equals (s)
& trans.To.Equals (t)).SingleOrDefault ();
if (transition != null)
sm.Add (transition);
}
}
var table = sm.BuildConversionTable ();
var A = sm.GetTransitionMatrix (table);
var b = new DenseVector (
sm.States.Select (x =>
Transitions.Where (y => y.From.Equals (x))
.Where (y => s1.Contains (y.To))
.Select (y => y.Probability).Sum ()
).ToArray ()
);
Console.WriteLine ("---------- [Conversion Table]");
Console.WriteLine (string.Join ("\n", table.Select (x => x.Key + ":" + x.Value)));
Console.WriteLine ("----------");
Console.WriteLine ("---------- [A]");
Console.WriteLine (A);
Console.WriteLine ("----------");
Console.WriteLine ("---------- [b]");
Console.WriteLine (b);
Console.WriteLine ("----------");
var epsilon = 0.001;
MathNet.Numerics.LinearAlgebra.Generic.Vector<double> prevsol = new DenseVector (b.Count, 0);
MathNet.Numerics.LinearAlgebra.Generic.Vector<double> currentsol = new DenseVector (b.Count, 0);
do {
prevsol = currentsol;
currentsol = A.Multiply (prevsol) + b;
} while ((prevsol - currentsol).AbsoluteMaximum() > epsilon);
Console.WriteLine ("---------- [solution]");
Console.WriteLine (currentsol);
Console.WriteLine ("----------");
foreach (var s in spending)
caching[until].Add(s, currentsol[table[s.Identifier]]);
Console.WriteLine ("---------- [Final result]");
Console.WriteLine (string.Join ("\n", caching[until].Select (x => x.Key.Identifier + " : " + x.Value)));
Console.WriteLine ("----------");
}
return caching[until][currentState];
}
