public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env, bool init = true)
{
if (init) {
var allVariables = new List<Variable>();
if (formula is Variable) allVariables.Add((Variable)formula);
allVariables.AddRange(formula.AllSubFormulas.OfType<Variable>());
allVariables.AddRange(formula.AllSubFormulas.OfType<Mu>().Select(mu => mu.Variable));
allVariables.AddRange(formula.AllSubFormulas.OfType<Nu>().Select(nu => nu.Variable));
Init(allVariables.Distinct(), lts, env);
}
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env, false)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env, false);
var rightStates = Solve(conj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env, false);
var rightStates = Solve(disj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env, false);
var hashSet = new HashSet<LTSState>();
foreach (var state in lts.States) {
var outTransitions = state.GetOutTransitions(box.RegularFormula);
if (outTransitions.All(tr => fe.Contains(tr.Right)))
hashSet.Add(state);
}
return hashSet;
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env, false);
}
else if (formula is Mu) {
var mu = formula as Mu;
if (mu.Parent is Nu) {
// surrounding binder is nu
// reset open subformulae of form mu Xk.g set env[k]=false
foreach (var innerMu in formula.AllSubFormulas.OfType<Mu>().Where(m => m.FreeVariables.Count > 0))
env[innerMu.Variable] = new HashSet<LTSState>();
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(mu.Variable);
env[mu.Variable] = Solve(mu.Formula, lts, env, false);
} while (Xold.Count != env[mu.Variable].Count);
return env[mu.Variable];
}
else if (formula is Nu) {
var nu = formula as Nu;
if (nu.Parent is Mu) {
// surrounding binder is mu
// reset open subformulae of form nu Xk.g set env[k]=true
foreach (var innerNu in formula.AllSubFormulas.OfType<Nu>().Where(m => m.FreeVariables.Count > 0))
env[innerNu.Variable] = lts.States;
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(nu.Variable);
env[nu.Variable] = Solve(nu.Formula, lts, env, false);
} while (Xold.Count != env[nu.Variable].Count);
return env[nu.Variable];
}
throw new InvalidDataException("formula not valid in our grammar");
}
public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env)
{
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env);
var rightStates = Solve(conj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env);
var rightStates = Solve(disj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env);
return new HashSet<LTSState>(lts.States.Where(
// states where, for all outtransitions with action a, the Formula holds in the direct successor
state => state.GetOutTransitions(box.RegularFormula).All(tr => fe.Contains(tr.Right))
));
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env);
}
else if (formula is Mu) {
var mu = formula as Mu;
env[mu.Variable] = new HashSet<LTSState>();
return FixedPoint.LFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(mu.Formula, lts, env);
env[mu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
else if (formula is Nu) {
var nu = formula as Nu;
env[nu.Variable] = lts.States;
return FixedPoint.GFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(nu.Formula, lts, env);
env[nu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
throw new InvalidDataException("not a valid formula in our grammar");
}
