Petri Nets Are Dioids

Authors:
Paolo Baldan;Fabio Gadducci
Affiliations:
Dipartimento di Matematica Pura e Applicata, Università Padova, Padova, Italia 35121;Dipartimento di Informatica, Università di Pisa, Polo "Guglielmo Marconi", La Spezia, Italia 19100
Venue:
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Year:
2008

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Abstract

In a seminal paper Montanari and Meseguer showed that an algebraic interpretation of Petri nets in terms of commutative monoids can be used to provide an elegant characterisation of the deterministic computations of a net, accounting for their sequential and parallel composition. Here we show that, along the same lines, by adding an (idempotent) operation and thus taking dioids (commutative semirings) rather than monoids, one can faithfully characterise the non-deterministic computations of a Petri net.