Towards a characterisation of finite-state message-passing systems

Abstract

We investigate an automata-theoretic model of distributed systems which communicate via message-passing. Each node in the system is a finite-state device. Channels are assumed to be reliable but may deliver messages out of order. Hence, each channel is modelled as a set of counters, one for each type of message. These counters may not be tested for zero. Though each node in the network is finite-state, the overall system is potentially infinite-state because the counters are unbounded. We work in an interleaved setting where the interactions of the system with the environment are described as sequences. The behaviour of a system is described in terms of the language which it accepts--that is, the set of valid interactions with the environment that are permitted by the system. Our aim is to characterise the class of message-passing systems whose behaviour is finite-state. Our main result is that the language accepted by a message-passing system is regular if and only if both the language and its complement are accepted by message-passing systems. We also exhibit an alternative characterisation of regular message-passing languages in terms of deterministic automata.