Configuration Structures, Event Structures and Petri Nets

TL;DR

This paper extends the correspondence between Petri nets and event structures to more general nets without self-loops, introducing new event structures and relating them through configuration structures to better understand their behavior.

Contribution

It proposes a more general form of event structures matching the expressive power of arbitrary nets without self-loops and relates them via configuration structures.

Findings

Characterization of classes of configuration structures by closure properties.

Axiomatization of propositional theories for event structures.

Structural properties of Petri nets linked to configuration structures.

Abstract

In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure. A configuration structure can also be considered logically, as a class of propositional models, or - equivalently - as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net. For a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties, as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms, and in terms of structural properties of the associated Petri nets.