
Hi,
I would like to encode a routing problem using z3.
So simplifiedt he problem is the following:
 I have a number of Nodes that are connected with each other by edges
 Each edge has a weight, that is basically the communication cost
 I would like to encode the topology only by provindng the cost for the neihbours
 The cost of should be calculated over a transitive relation, but i m not sure how to encode this.
 In the example i have a very simple topology consisting of 4 nodes, x, y,z, v and they are connected like: x>y>z>v
so i want z3 to find automatically the cost of communication between x and v, which should be the sum of the edges in between. Is there a elegant way to encode this?
Maybe there is a smarter way to encode such routing problem .. do u have any examples?
Here the start of my encoding:
(declaresort A)
(declareconst x A)
(declareconst y A)
(declareconst z A)
(declareconst v A)
(declarefun path (A A) Int)
(assert (= (path x y) 1))
(assert (= (path y z) 2))
(assert (= (path z v) 3))
(checksat)
(getmodel)



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