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.