Concurrent behaviour: Sequences, processes and axioms

Abstract

Two ways of describing the behaviour of concurrent systems have widely been suggested: arbitrany interleaving and partial orders. Sometimes the latter has been claimed superior because concurrency is represented in a "true" way; on the other hand, some authors have claimed that the former is sufficient for all practical purposes.Petri net theory offers a framework in which both kinds of semantics can be defined formally and hence compared with each other. Firing sequences correspond to interleaved behaviour while the notion of a process is used to capture partial order semantics. For most concurrent programming languages such as CSP or shared variable languages, sequence semantics is widely used but little work exists on process semantics.This paper aims at obtaining formal results about the relationship between processes and firing sequences in net theory. We show that generally speaking, the class of behaviours defined by the two semantics is the same, but that it is difficult to find a "nice" relationship between sequences and processes. We also discuss one of the process axioms which is particularly interesting on intuitive grounds. Finally, we define the notion of a process also for concurrent programming languages, thus providing the basis to do similar analyses as have been done in net theory.