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A Toolchain to Compute Concurrent Places of Petri Nets

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Transactions on Petri Nets and Other Models of Concurrency XVII

Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 14150))

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Abstract

The concurrent places of a Petri net are all pairs of places that may simultaneously have a token in some reachable marking. Concurrent places generalize the usual notion of dead places and are particularly useful for decomposing a Petri net into synchronized automata executing in parallel. We present a state-of-the-art toolchain to compute the concurrent places of a Petri net. This is achieved by a rich combination of various techniques, including: state-space exploration using BDDs, structural rules for concurrent places, quadratic over- and under-approximation of reachable markings, and polyhedral abstraction of the state space based on structural reductions and linear arithmetic constraints on markings. We assess the performance of our toolchain on a large collection of 850 nets originating from the 2022 edition of the Model Checking Contest.

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Notes

  1. 1.

    https://cadp.inria.fr.

  2. 2.

    https://github.com/nicolasAmat/Kong.

  3. 3.

    https://pnml.lip6.fr/pnml2nupn.

  4. 4.

    https://projects.laas.fr/tina.

  5. 5.

    https://mcc.lip6.fr/2022/nupn.php.

  6. 6.

    https://cadp.inria.fr/man/nupn.html.

  7. 7.

    When unit-safeness is known by construction, or if it has been proven later.

  8. 8.

    https://projects.laas.fr/tina/manuals/ndrio.html.

  9. 9.

    https://cadp.inria.fr/man/caesar.bdd.html.

  10. 10.

    https://cadp.inria.fr/man/caesar.bdd.html.

  11. 11.

    In this method, singletons are also considered as pairs \(\{ p, p \}\).

  12. 12.

    https://github.com/nicolasAmat/Kong.

  13. 13.

    https://mcc.lip6.fr/2022/models.php.

  14. 14.

    This succeeded for all the nets considered here, although, in general, unit-safeness may be difficult to determine for large nets.

  15. 15.

    https://www.grid5000.fr.

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Acknowledgements

Experiments presented in this paper were carried out using the Grid’5000 testbed, supported by a scientific interest group hosted by Inria and including Cnrs, Renater, and several Universities as well as other organizations. We are grateful to Lom Messan Hillah for his Pnml2Nupn translator, to Fabio Somenzi for providing us with the latest version 3.1.0 of Cudd, to Bernard Berthomieu for providing the tool Reduce, and to Silvano Dal Zilio and Didier Le Botlan for their contributions to Kong.

Author information

Authors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, CNRS, INSA, Toulouse, France

    Nicolas Amat

  2. Univ. Grenoble Alpes, INRIA, CNRS, Grenoble INP LIG, Grenoble, France

    Pierre Bouvier & Hubert Garavel

Authors
  1. Nicolas Amat
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  2. Pierre Bouvier
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  3. Hubert Garavel
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Corresponding author

Correspondence to Nicolas Amat .

Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Maciej Koutny

  2. Fakultät Zentralbereich, FernUniversität in Hagen, Hagen, Nordrhein-Westfalen, Germany

    Robin Bergenthum

  3. Dept of Computer Science, Iowa State University, Ames, IA, USA

    Gianfranco Ciardo

A Run-Length-Encoding Compression

A Run-Length-Encoding Compression

As mentioned in Sect. 2.3, each line of the concurrency matrix is compressed using a simple run-length-encoding scheme: any sequence of \(n>3\) consecutive identical characters is replaced by a single character followed by the value of n enclosed between parentheses. For instance, the following sequence of 18 characters: “10000..........001” is replaced by a sequence of 13 characters: “10(4).(10)001”. Table 4 illustrates the compression of an entire matrix, and Table 5 gives an implementation in C of the compression and decompression algorithms (which we also implemented in Awk, Python, and Bourne shell).

This scheme enjoys three nice properties: (i) the size (in characters) of the compressed output is always less or equal to the size of the input; in practice, we observed a reduction factor of 214 (mean value) up to 4270 (maximal value) measured on 12,671 NUPNs; (ii) compressing an already compressed input has no effect; (iii) compression and decompression can operate on the fly (e.g., using coroutines, pipes, or data streams), meaning that it is not mandatory to generate a matrix entirely before starting to compress it, and that one can compare two (or more) compressed matrices without having to decompress them entirely in advance.

Table 5. Decompression (left) and compression (right) algorithms.
Full size table

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Amat, N., Bouvier, P., Garavel, H. (2024). A Toolchain to Compute Concurrent Places of Petri Nets. In: Koutny, M., Bergenthum, R., Ciardo, G. (eds) Transactions on Petri Nets and Other Models of Concurrency XVII. Lecture Notes in Computer Science(), vol 14150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-68191-6_1

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  • DOI: https://doi.org/10.1007/978-3-662-68191-6_1

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