Verifying identical communicating processes is undecidable

Abstract

We prove that boundedness and reachability tree finiteness are undecidable for systems of two identical automata communicating via two perfect unbounded one-way FIFO channels and constructed solely from cycles about their initial states. Using a form of mutual exclusion for such systems, we prove further that undecidability holds even when the identical automata are totally indistinguishable in the sense that their initial states are identical and both channels are initially empty.