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Abstract: In this paper the correspondence between safe Petri nets and eventstructures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary netswithout self-loops, under the collective token interpretation. To this end wepropose a more general form of event structure, matching the expressive powerof such nets. These new event structures and nets are connected by relatingboth notions with configuration structures, which can be regarded asrepresentations of either event structures or nets that capture their behaviourin terms of action occurrences and the causal relationships between them, butabstract from any auxiliary structure.A configuration structure can also be considered logically, as a class ofpropositional models, or - equivalently - as a propositional theory indisjunctive normal from. Converting this theory to conjunctive normal form isthe key idea in the translation of such a structure into a net.For a variety of classes of event structures we characterise the associatedclasses of configuration structures in terms of their closure properties, aswell as in terms of the axiomatisability of the associated propositionaltheories by formulae of simple prescribed forms, and in terms of structuralproperties of the associated Petri nets.



Author: R.J. van Glabbeek, G.D. Plotkin

Source: https://arxiv.org/







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