Ring Networks Are Easier to Verify ? (report)

We show in this paper how the ring topology makes easier the analysis of communicating nite state machines' reachability set. We prove that the analysis of this kind of systems can be reduced to the analysis of a single automaton with a single queue. This leads us, by the use of new symbolic transitions, to the proposal of two semi-algorithms, one for normal ring networks and one for lossy ring networks. In the case of normal ring networks, the proposed semi-algorithm is simpler and more general than those of BGWW97] and BH97]. In particular, the time complexity of its key steps is polynomial whereas those of BGWW97] and BH97] have not been investigated and should not be polynomial (the one of BH97] uses Pressburger arithmetic which induces a double exponential time complexity). The semi-algorithm for lossy ring networks is a simple application of this for normal ring networks and is however more general than that of ABJ98]. Furthermore, quite immediate consequences of the techniques we use are: (a) the reachability set of a ring network which at least one queue is a counter is constructively recognizable; (b) the reachability problem is decidable for ring networks with at least one lossy queue.