public AllGlobalProposition(int numStates, IProposition f)
{
this.f = f;
// AG(f) === !EF(!f)
var notF = new NotProposition(f);
this.existsFuture = new ExistsFutureProposition(numStates, notF);
}
public void AlternatingBitProtocolSender()
{
// 0* --> 1 <-> 2 g* --> s <-> w
// ^ | ^ |
// | v | v
// 5 <-> 4 <-- 3* bw <-> bs <-- bg*
const int numNodes = 6;
var ts = new TransitionSystem(numNodes);
ts.AddTransition(0, 0);
ts.AddTransition(0, 1);
ts.AddTransition(1, 2);
ts.AddTransition(2, 1);
ts.AddTransition(2, 3);
ts.AddTransition(3, 3);
ts.AddTransition(3, 4);
ts.AddTransition(4, 5);
ts.AddTransition(5, 4);
ts.AddTransition(5, 0);
var initial = new[] { 0, 3 }; // initial states
var g = new Proposition(numNodes, "g"); // getting data from user
g.Set(0, 3);
var s = new Proposition(numNodes, "s"); // sending message
s.Set(1, 4);
var w = new Proposition(numNodes, "w"); // waiting for acknowledgement
w.Set(2, 5);
var b = new Proposition(numNodes, "b"); // control bit
b.Set(3, 4, 5);
using (var writer = new StringWriter())
{
ts.ExportToGraphviz(writer, new[] { g, s, w, b });
Debug.Log(writer);
}
// AG(s || w || g) -- the sender is always in one of these three states
var or1 = new OrProposition(s, w);
var or2 = new OrProposition(or1, g);
var ag = new AllGlobalProposition(numNodes, or2);
Debug.Log(ag);
Assert.IsTrue(ag.Evaluate(ts, initial));
// EG(!s && !w) -- there is a path where the sender is never sending nor waiting
var notS = new NotProposition(s);
var notW = new NotProposition(w);
var and = new AndProposition(notS, notW);
var eg = new ExistsGlobalProposition(numNodes, and);
Debug.Log(eg);
Assert.IsTrue(eg.Evaluate(ts, initial));
}
