Models for Concurrency

Abstract

This is a draft version of a chapter for the Handbook of Logic and the Foundations of Computer Science, Oxford University Press. The final draft can be found as DAIMI PB 463.
It surveys a range of models for parallel computation to include interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like Petri nets, asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. It is still a draft at present. In particular, the ''Notes'' surveying related work are incomplete and the appendix on fibred categories needs to be overhauled in the light of some slick proofs, provided by Bart Jacobs. It is ragged in other places too. Constructive comments and corrections will be appreciated.

A knowledge of basic category theory is assumed, up to an acquaintance with the notion of adjunction.