Deadlock detection by fair reachability analysis: from cyclic to multi-cyclic protocols (and beyond?)

We generalize the technique of fair reachability analysis to multi-cyclic protocols modeled as networks of communicating finite state machines, where a number of cyclic protocols are interconnected in such a way that any two component cyclic protocols share at most one process and each channel in the protocol belongs to exactly one component cyclic protocol. By composing the fair reachability relations of the component cyclic protocols, we prove that the set of fair reachable states of a multi-cyclic protocol is exactly the set of reachable states that are of equal channel length with respect to each of its component cyclic protocols. As a result, each deadlock state is fair reachable, and deadlock detection is decidable for the class of multi-cyclic protocols whose fair reachable state spaces are finite. Under the assumption that the underlying communication topology of a protocol is strongly connected, we show that fair reachability analysis is inherently infeasible for logical correctness validation beyond multi-cyclic protocols.