Minimisation of Event Structures

TL;DR

This paper develops a theory of minimisation for event structures, introducing foldings as behaviour-preserving quotients, and proves the existence and uniqueness of minimal quotients in various models.

Contribution

It introduces a general framework for minimising event structures via foldings, extending existing models and establishing conditions for minimal quotients.

Findings

Every event structure has a unique minimal quotient via folding.

Prime event structures always admit a unique minimal quotient.

Foldings of general event structures relate to foldings of prime event structures.

Abstract

Event structures are fundamental models in concurrency theory, providing a representation of events in computation and of their relations, notably concurrency, conflict and causality. In this paper we present a theory of minimisation for event structures. Working in a class of event structures that generalises many stable event structure models in the literature (e.g., prime, asymmetric, flow and bundle event structures), we study a notion of behaviour-preserving quotient, referred to as a folding, taking (hereditary) history preserving bisimilarity as a reference behavioural equivalence. We show that for any event structure a folding producing a uniquely determined minimal quotient always exists. We observe that each event structure can be seen as the folding of a prime event structure, and that all foldings between general event structures arise from foldings of (suitably defined) corresponding prime event structures. This gives a special relevance to foldings in the class of prime event structures, which are studied in detail. We identify folding conditions for prime and asymmetric event structures, and show that also prime event structures always admit a unique minimal quotient (while this is not the case for various other event structure models).