public void KeyDoor()
{
// process
//
// 0 <--door--> 1 <--door--> 2
// key x2
// transition system
//
// 1 --> 3*
// ^ |
// | v
// 0 5 --> 6*
// | ^
// v |
// 2 --> 4*
const int numNodes = 7;
var ts = new TransitionSystem(numNodes);
ts.AddTransition(0, 1);
ts.AddTransition(0, 2);
ts.AddTransition(1, 3);
ts.AddTransition(2, 4);
ts.AddTransition(3, 3);
ts.AddTransition(3, 5);
ts.AddTransition(4, 4);
ts.AddTransition(4, 5);
ts.AddTransition(5, 5);
ts.AddTransition(5, 6);
ts.AddTransition(6, 6);
var initial = new[] { 0 }; // initial states
var a = new Proposition(numNodes, "a"); // has a key
a.Set(1, 2, 5);
var b = new Proposition(numNodes, "b"); //key1 acquired
b.Set(1, 3, 5, 6);
var c = new Proposition(numNodes, "c"); // key2 acquired
c.Set(2, 4, 5, 6);
var d = new Proposition(numNodes, "d"); // door1 open
d.Set(3, 4, 5, 6);
var e = new Proposition(numNodes, "e"); //door2 open
e.Set(6);
var f = new Proposition(numNodes, "f"); // goal
f.Set(6);
using (var writer = new StringWriter())
{
ts.ExportToGraphviz(writer, new[] { a, b, c, d, e, f });
Debug.Log(writer);
}
// EF(f) -- there exists a path starting at the initial states where f eventually holds (goal is reachable)
var ef = new ExistsFutureProposition(numNodes, f);
Debug.Log(ef);
Assert.IsTrue(ef.Evaluate(ts, initial));
// AG(EF(f)) -- from all reachable states there exists a path to the goal
var ag = new AllGlobalProposition(numNodes, ef);
Debug.Log(ag);
Assert.IsTrue(ag.Evaluate(ts, initial));
}
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));
}
public void TransitionSystem()
{
const int numNodes = 7;
const int numBits = 3;
Assert.Less(numNodes, 1 << (numBits + 1));
var ts = new TransitionSystem(numNodes);
ts.AddTransition(0, 1);
ts.AddTransition(0, 2);
ts.AddTransition(1, 3);
ts.AddTransition(2, 4);
ts.AddTransition(3, 3);
ts.AddTransition(3, 5);
ts.AddTransition(4, 4);
ts.AddTransition(4, 5);
ts.AddTransition(5, 5);
ts.AddTransition(5, 6);
ts.AddTransition(6, 6);
var obdd = new OBDD();
var root = BDDNode.False;
for (int i = 0; i < numNodes; i++)
{
for (int j = 0; j < numNodes; j++)
{
if (!ts.HasTransition(i, j))
{
continue;
}
var transition = AddTransition(obdd, i, j, numBits);
root = obdd.MakeOr(root, transition);
}
}
using (var writer = new StringWriter())
{
ts.ExportToGraphviz(writer, new IProposition[0]);
Debug.Log(writer);
}
using (var writer = new StringWriter())
{
root.ExportToGraphviz(writer);
Debug.Log(writer);
}
using (var writer = new StringWriter())
{
obdd.ExportToGraphviz(writer);
Debug.Log(writer);
}
}