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Petri Nets Are Dioids

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Algebraic Methodology and Software Technology (AMAST 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5140))

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.

Supported by the EU IST-2004-16004 SEnSOria and the MIUR Project ART.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università Padova, Via Trieste 63, 35121, Padova, Italia

    Paolo Baldan

  2. Dipartimento di Informatica, Università di Pisa, Polo “Guglielmo Marconi”, via dei Colli 90, 19100, La Spezia, Italia

    Fabio Gadducci

Authors
  1. Paolo Baldan
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  2. Fabio Gadducci
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José Meseguer Grigore Roşu

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Baldan, P., Gadducci, F. (2008). Petri Nets Are Dioids. In: Meseguer, J., Roşu, G. (eds) Algebraic Methodology and Software Technology. AMAST 2008. Lecture Notes in Computer Science, vol 5140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79980-1_5

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  • DOI: https://doi.org/10.1007/978-3-540-79980-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79979-5

  • Online ISBN: 978-3-540-79980-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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