Symbolic verification of infinite systems using a finite union of DFAs

We address the verification problem of FIFO channel systems by applying the symbolic analysis principle. Communication protocols can be modelled by a finite set of finite-state machines (CFSMs) that communicate between each other by exchanging messages via unbounded FIFO channels/queues. A Finite Union of Deterministic Finite Automata (FUDFA) is used to represent (possibly) infinite set of queue contents. Quite a few operations needed to symbolically analyze such systems can be implemented on the union of DFAs in polynomial time. The advantage gained by this approach is that the inclusion between finite unions DFAs can be checked efficiently. We show that FUDFAs can be used for the for-ward and backward reachability analysis of the systems. It also lifts this approach for the case of a protocol with n queues. We use this fact to define a generic reachability analysis semi-algorithm parameterized by a set of cycles Θ. Given a set of configurations, this semi-algorithm performs a least fix-point calculation to construct the set of its successors (or predecessors). At each step, the search is accelerated by considering the cycles in Θ as additional "meta-transitions", an approach adopted similar in nature to that proposed by Boigelot and Godefroid.