Conflict vs Causality in Event Structures

TL;DR

This paper analyzes how simplifying event structures by removing causality or conflict relations affects the spectrum of behavioral equivalences, revealing that removing causality simplifies the spectrum more than removing conflict.

Contribution

It provides a detailed comparison of equivalence spectra in simplified event structures, highlighting the impact of causality and conflict removal on behavioral equivalences.

Findings

Removing causality simplifies the spectrum more than removing conflict.

Labeling and event set size influence equivalences in conflict-free structures.

Simplified models lead to a collapse of some equivalence distinctions.

Abstract

Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting.