Symbolic Reachability Analysis of FIFO - ChannelSystems with Nonregular Sets

We address the veriication problem of FIFO-channel systems by applying the symbolic analysis principle. We represent their sets of states (conngurations) using structures called CQDD's combining nite-state automata with linear constraints on number of occurrences of symbols. We show that CQDD's allow forward and backward reachability analysis of systems with nonregular sets of conngurations. Moreover, we prove that CQDD's allow to compute the exact eeect of the repeated execution of any xed cycle in the transition graph of a system. We use this fact to deene a generic reachability analysis semi-algorithm parametrized by a set of cycles. Given a set of conngurations, this semi-algorithm performs a least xpoint calculation to construct the set of its successors (or predecessors). At each step, this calculation is accelerated by considering the cycles in as additional \meta-transitions" in the transition graph, generalizing the approach adopted in 5].