Robust asynchronous protocols are finite-state

Abstract

We consider networks of finite-state machines which communicate over reliable channels which may reorder messages. Each machine in the network also has a local input tape. Since channels are unbounded, the network as a whole is, in general, infinite-state. An asynchronous protocol is a network equipped with an acceptance condition. Such a protocol is said to be robust if it never deadlocks and, moreover, it either accepts or rejects each input in an unambiguous manner. The behaviour of a. robust protocol is insensitive to nondeterminism introduced by either message reordering or the relative speeds at which components read their local inputs. Using an automata-theoretic model, we show that, at a global level, every robust asynchronous protocol has a finite-state representation To prove this, we establish a variety of pumping lemmas. We also demonstrate a distributed language which does not admit a robust protocol.