Petri nets are dioids: a new algebraic foundation for non-deterministic net theory View Full Text


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Article Info

DATE

2019-02

AUTHORS

Paolo Baldan, Fabio Gadducci

ABSTRACT

In a seminal paper Montanari and Meseguer have shown 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. A smoother and more complete theory for deterministic computations has been later developed by relying on the concept of pre-net, a variation of Petri nets with a non-commutative flavor. This paper shows that, along the same lines, by adding an (idempotent) operation and thus considering dioids (idempotent semirings) rather than just monoids, one can faithfully characterise the non-deterministic computations of a net. More... »

PAGES

1-32

References to SciGraph publications

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  • 1996-10. Axiomatizing the algebra of net computations and processes in ACTA INFORMATICA
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  • 2008. Petri Nets Are Dioids in ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY
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  • 1999-12. An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories in APPLIED CATEGORICAL STRUCTURES
  • 2010-07-05. A Survey of Graphical Languages for Monoidal Categories in NEW STRUCTURES FOR PHYSICS
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  • Journal

    TITLE

    Acta Informatica

    ISSUE

    N/A

    VOLUME

    N/A

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00236-018-0314-0

    DOI

    http://dx.doi.org/10.1007/s00236-018-0314-0

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1100587663


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