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Petri Nets and Semilinear Sets (Extended Abstract)

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Theoretical Aspects of Computing – ICTAC 2016 (ICTAC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9965))

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Abstract

Semilinear sets play a key role in many areas of computer science, in particular, in theoretical computer science, as they are characterizable by Presburger Arithmetic (a decidable theory). The reachability set of a Petri net is not semilinear in general. There are, however, a wide variety of subclasses of Petri nets enjoying semilinear reachability sets, and such results as well as analytical techniques developed around them contribute to important milestones historically in the analysis of Petri nets. In this talk, we first give a brief survey on results related to Petri nets with semilinear reachability sets. We then focus on a technique capable of unifying many existing semilinear Petri nets in a coherent way. The unified strategy also leads to various new semilinearity results for Petri nets. Finally, we shall also briefly touch upon the notion of almost semilinear sets which witnesses some recent advances towards the general Petri net reachability problem.

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Authors and Affiliations

  1. Department of Electrical Engineering, National Taiwan University, Taipei, 106, Taiwan, Republic of China

    Hsu-Chun Yen

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  1. Hsu-Chun Yen
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Correspondence to Hsu-Chun Yen .

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Editors and Affiliations

  1. Universidade Federal de Pernambuco Centro de Informática, Recife, Pernambuco, Brazil

    Augusto Sampaio

  2. Deptartment of Electrical Engineering BL, National Taiwan University, Taipei, Taiwan

    Farn Wang

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Yen, HC. (2016). Petri Nets and Semilinear Sets (Extended Abstract). In: Sampaio, A., Wang, F. (eds) Theoretical Aspects of Computing – ICTAC 2016. ICTAC 2016. Lecture Notes in Computer Science(), vol 9965. Springer, Cham. https://doi.org/10.1007/978-3-319-46750-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-46750-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46749-8

  • Online ISBN: 978-3-319-46750-4

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