private double CalculateProbabilityToReachStateFormula(Formula psi)
{
// calculate P [true U psi]
var psiEvaluator = MarkovChain.CreateFormulaEvaluator(psi);
var precalculatedStates = CreateEmptyPrecalculatedStatesArray();
CalculateSatisfiedStates(precalculatedStates, psiEvaluator);
//CalculateExcludedStates(precalculatedStates); // change for \phi Until \psi
// calculate probabilityExactlyZero (prob0)
ProbabilityExactlyZero(precalculatedStates);
// calculate probabilityExactlyOne (prob1)
ProbabilityExactlyOne(precalculatedStates);
//TODO: Do not calculate exact state probabilities, when _every_ initial state>0 is either in probabilityExactlyZero or in probabilityExactlyOne
var derivedMatrix = CreateDerivedMatrix(precalculatedStates);
var derivedVector = CreateDerivedVector(precalculatedStates, PrecalculatedState.ExaclyOneForFinally);
var resultVector = GaussSeidel(derivedMatrix, derivedVector, 50);
var finalProbability = CalculateFinalProbability(resultVector);
return(finalProbability);
}
private double CalculateProbabilityToReachStateFormula(Formula psi)
{
// calculate P [true U psi]
var psiEvaluator = MarkovChain.CreateFormulaEvaluator(psi);
var directlySatisfiedStates = CalculateSatisfiedStates(psiEvaluator);
var excludedStates = new Dictionary <long, bool>(); // change for \phi Until \psi. For classical "Finally", no states are excluded
// calculate probabilityExactlyZero (prob0)
var probabilityExactlyZero = ProbabilityExactlyZero(directlySatisfiedStates, excludedStates);
// calculate probabilityExactlyOne (prob1)
var probabilityExactlyOne = ProbabilityExactlyOne(directlySatisfiedStates, excludedStates, probabilityExactlyZero);
//TODO: Do not calculate exact state probabilities, when _every_ initial state>0 is either in probabilityExactlyZero or in probabilityExactlyOne
var derivedMatrix = CreateDerivedMatrix(probabilityExactlyOne, probabilityExactlyZero);
var derivedVector = CreateDerivedVector(probabilityExactlyOne);
var resultVector = GaussSeidel(derivedMatrix, derivedVector, 50);
var finalProbability = CalculateFinalProbability(resultVector);
return(finalProbability);
}
private double CalculateProbabilityToReachStateFormulaInBoundedSteps(Formula psi, Formula phi, int steps)
{
// Pr[phi U psi]
// calculate P [true U<=steps psi]
var stopwatch = new Stopwatch();
stopwatch.Start();
var psiEvaluator = MarkovChain.CreateFormulaEvaluator(psi);
var stateCount = MarkovChain.States;
var directlySatisfiedStates = CalculateSatisfiedStates(psiEvaluator);
Dictionary <long, bool> excludedStates;
if (phi == null)
{
excludedStates = new Dictionary <long, bool>();
}
else
{
// excludedStates = Sat(\phi) \Cup Sat(psi)
var phiEvaluator = MarkovChain.CreateFormulaEvaluator(phi);
var phiOrPsiStates = CalculateSatisfiedStates(phiEvaluator);
foreach (var directlySatisfiedState in directlySatisfiedStates)
{
phiOrPsiStates[directlySatisfiedState.Key] = true;
}
excludedStates = CreateComplement(phiOrPsiStates);
}
var enumerator = MarkovChain.GetEnumerator();
var xold = new double[stateCount];
var xnew = CreateDerivedVector(directlySatisfiedStates);
var loops = 0;
while (loops < steps)
{
// switch xold and xnew
var xtemp = xold;
xold = xnew;
xnew = xtemp;
loops++;
for (var i = 0; i < stateCount; i++)
{
if (directlySatisfiedStates.ContainsKey(i))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 1.0;
}
else if (excludedStates.ContainsKey(i))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 0.0;
}
else
{
enumerator.SelectSourceState(i);
var sum = 0.0;
while (enumerator.MoveNextTransition())
{
var entry = enumerator.CurrentTransition;
sum += entry.Value * xold[entry.Column];
}
xnew[i] = sum;
}
}
if (loops % 10 == 0)
{
stopwatch.Stop();
var currentProbability = CalculateFinalProbability(xnew);
_output?.WriteLine($"{loops} Bounded Until iterations in {stopwatch.Elapsed}. Current probability={currentProbability.ToString(CultureInfo.InvariantCulture)}");
stopwatch.Start();
}
}
var finalProbability = CalculateFinalProbability(xnew);
stopwatch.Stop();
return(finalProbability);
}
private double CalculateUnboundUntil(Formula psi, Formula phi, int iterationsLeft)
{
// On algorithmic verification methods for probabilistic systems (1998) by Christel Baier
// Theorem 3.1.6 (page 36)
// http://wwwneu.inf.tu-dresden.de/content/institutes/thi/algi/publikationen/texte/15_98.pdf
// Pr[phi U psi]
// calculate P [true U<=steps psi]
var stopwatch = new Stopwatch();
stopwatch.Start();
var psiEvaluator = MarkovChain.CreateFormulaEvaluator(psi);
var stateCount = MarkovChain.States;
var fixPointReached = iterationsLeft <= 0;
var directlySatisfiedStates = CalculateSatisfiedStates(psiEvaluator);
Dictionary <long, bool> excludedStates;
if (phi == null)
{
excludedStates = new Dictionary <long, bool>();
}
else
{
// excludedStates = Sat(\phi) \Cup Sat(psi)
var phiEvaluator = MarkovChain.CreateFormulaEvaluator(phi);
var phiOrPsiStates = CalculateSatisfiedStates(phiEvaluator);
foreach (var directlySatisfiedState in directlySatisfiedStates)
{
phiOrPsiStates[directlySatisfiedState.Key] = true;
}
excludedStates = CreateComplement(phiOrPsiStates);
}
// calculate probabilityExactlyZero (prob0)
var probabilityExactlyZero = ProbabilityExactlyZero(directlySatisfiedStates, excludedStates);
// calculate probabilityExactlyOne (prob1)
var probabilityExactlyOne = ProbabilityExactlyOne(directlySatisfiedStates, excludedStates, probabilityExactlyZero);
var enumerator = MarkovChain.GetEnumerator();
var xold = new double[stateCount];
var xnew = CreateDerivedVector(probabilityExactlyOne);
var loops = 0;
while (!fixPointReached)
{
// switch xold and xnew
var xtemp = xold;
xold = xnew;
xnew = xtemp;
iterationsLeft--;
loops++;
for (var i = 0; i < stateCount; i++)
{
if (probabilityExactlyOne.ContainsKey(i))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 1.0;
}
else if (probabilityExactlyZero.ContainsKey(i))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 0.0;
}
else
{
enumerator.SelectSourceState(i);
var sum = 0.0;
while (enumerator.MoveNextTransition())
{
var entry = enumerator.CurrentTransition;
sum += entry.Value * xold[entry.Column];
}
xnew[i] = sum;
}
}
if (loops % 10 == 0)
{
stopwatch.Stop();
var currentProbability = CalculateFinalProbability(xnew);
_output?.WriteLine($"{loops} Fixpoint Until iterations in {stopwatch.Elapsed}. Current probability={currentProbability.ToString(CultureInfo.InvariantCulture)}");
stopwatch.Start();
}
if (iterationsLeft <= 0)
{
fixPointReached = true;
}
}
var finalProbability = CalculateFinalProbability(xnew);
stopwatch.Stop();
return(finalProbability);
}
private double CalculateProbabilityToReachStateFormulaInBoundedSteps(Formula psi, int steps)
{
// calculate P [true U<=steps psi]
var stopwatch = new Stopwatch();
stopwatch.Start();
var psiEvaluator = MarkovChain.CreateFormulaEvaluator(psi);
var stateCount = MarkovChain.States;
var precalculatedStates = CreateEmptyPrecalculatedStatesArray();
CalculateSatisfiedStates(precalculatedStates, psiEvaluator);
//CalculateExcludedStates(precalculatedStates); // change for \phi Until \psi
var enumerator = MarkovChain.GetEnumerator();
var xold = new double[stateCount];
var xnew = CreateDerivedVector(precalculatedStates, PrecalculatedState.Satisfied);
var loops = 0;
while (loops < steps)
{
// switch xold and xnew
var xtemp = xold;
xold = xnew;
xnew = xtemp;
loops++;
for (var i = 0; i < stateCount; i++)
{
if (precalculatedStates[i].HasFlag(PrecalculatedState.Satisfied))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 1.0;
}
else if (precalculatedStates[i].HasFlag(PrecalculatedState.Excluded))
{
//we could remove this line, because already set by CreateDerivedVector and never changed when we initialize xold with CreateDerivedVector(directlySatisfiedStates)
xnew[i] = 0.0;
}
else
{
enumerator.SelectSourceState(i);
var sum = 0.0;
while (enumerator.MoveNextTransition())
{
var entry = enumerator.CurrentTransition;
sum += entry.Value * xold[entry.Column];
}
xnew[i] = sum;
}
}
if (loops % 10 == 0)
{
stopwatch.Stop();
var currentProbability = CalculateFinalProbability(xnew);
_output?.WriteLine($"{loops} Bounded Until iterations in {stopwatch.Elapsed}. Current probability={currentProbability.ToString(CultureInfo.InvariantCulture)}");
stopwatch.Start();
}
}
var finalProbability = CalculateFinalProbability(xnew);
stopwatch.Stop();
return(finalProbability);
}