Structure of concurrency

Abstract

Noninterleaving models of concurrency assume that behavioural properties of systems can be adequately modelled in terms of causal partial orders. We claim that the structure of concurrency is richer, with causality being only one of the invariants generated by a set of closely related executions or observations. The model we propose supports three levels of abstraction: the observation level, invariant level and system level; and we will proceed from the bottom (observation) level to the top (system) level. This is in contrast to the way other models for concurrency are introduced, as they essentially support two levels of abstraction, the system level and behavioural level (which includes both observations and invariants), with the direction of development going from the system to behavioural level. In this paper we first discuss the notion of an observation of a concurrent behaviour; in particular, we investigate the role played by interval partial orders. We then introduce a general framework for dealing with invariants generated by sets of closely related observations. This leads to the formulation of the notion of a (concurrent) history whose structural properties are subsequently studied.