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Transactions on Petri Nets and Other Models of Concurrency XI pp 137–159Cite as

Conditions for Petri Net Solvable Binary Words

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Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 9930))

Abstract

A word is called Petri net solvable if it is isomorphic to the reachability graph of an unlabelled Petri net. In this paper, the class of finite, two-letter, Petri net solvable, words is studied. Two conjectures providing different characterisations of this class of words are motivated and proposed. One conjecture characterises the class in terms of pattern-matching, the other in terms of letter-counting. Several results are described which amount to a partial proof of these conjectures.

K. Barylska, Ł. Mikulski and M. Piątkowski—Supported by the Polish Nat. Sci. Center (grant no. 2013/09/D/ST6/03928).

E. Best and E. Erofeev—Supported by DFG CAVER, ARS, and http://www.uni-oldenburg.de/en/scare/.

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Acknowledgments

We would like to thank Raymond Devillers, Thomas Hujsa, Uli Schlachter and Harro Wimmel for valuable comments. We also thank the anonymous reviewers for their remarks which allowed to improve the presentation of the paper.

Note added in proof. This paper extends [2] by Sect. 5 and a few other enhancements. At the time of revision (May 2016), the conjectures stated in Sects. 3.3 and 4.2 have been proved correct. These proofs are contained in [5, 9].

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Authors and Affiliations

  1. Parallel Systems, Department of Computing Science, Carl von Ossietzky Universität, 26111, Oldenburg, Germany

    Eike Best & Evgeny Erofeev

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 87-100, Toruń, Poland

    Kamila Barylska, Łukasz Mikulski & Marcin Piątkowski

Authors
  1. Kamila Barylska
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  2. Eike Best
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  3. Evgeny Erofeev
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  4. Łukasz Mikulski
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  5. Marcin Piątkowski
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Corresponding author

Correspondence to Eike Best .

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Editors and Affiliations

  1. Newcastle University , Newcastle upon Tyne, United Kingdom

    Maciej Koutny

  2. FernUniversität in Hagen , Hagen, Germany

    Jörg Desel

  3. Leiden University , Leiden, The Netherlands

    Jetty Kleijn

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Barylska, K., Best, E., Erofeev, E., Mikulski, Ł., Piątkowski, M. (2016). Conditions for Petri Net Solvable Binary Words. In: Koutny, M., Desel, J., Kleijn, J. (eds) Transactions on Petri Nets and Other Models of Concurrency XI. Lecture Notes in Computer Science(), vol 9930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53401-4_7

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  • DOI: https://doi.org/10.1007/978-3-662-53401-4_7

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