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Acta Informatica

, Volume 56, Issue 1, pp 61–92 | Cite as

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

  • Paolo Baldan
  • Fabio GadducciEmail author
Original Article
  • 203 Downloads

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.

Notes

Acknowledgements

We are indebted to Professor Peter May for the interaction and the fruitful discussions on bimonoidal categories, as well as to the reviewers for their remarks and pointers to the literature.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PadovaPaduaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaPisaItaly

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