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“Truly concurrent” and nondeterministic semantics of discrete-time Petri nets

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Abstract

In the paper, a “truly concurrent” and nondeterministic semantics is defined in terms of branching processes of discrete-time Petri nets (DTPNs). These nets may involve infinite numbers of transitions and places, infinite number of tokens in places, and (maximal) steps of concurrent transitions, which allows us to consider this class of DTPNs to be the most powerful class of Petri nets. It is proved that the unfolding (maximal branching process) of the DTPN is the greatest element of a complete lattice constructed on branching processes of DTPNs with step semantics. Moreover, it is shown that this result is true also in the case of maximal transition steps if additional restrictions are imposed on the structure and behavior of the DTPN.

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Authors and Affiliations

  1. A. P. Ershov Institute of Informatics Systems, Siberian Division, Russian Academy of Sciences, pr. akademika Lavrent’eva 6, Novosibirsk, 630090, Russia

    I. B. Virbitskaite

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    I. B. Virbitskaite & V. A. Borovlev

  3. Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    L. Popova-Zeugmann

Authors
  1. I. B. Virbitskaite
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  2. V. A. Borovlev
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  3. L. Popova-Zeugmann
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Correspondence to I. B. Virbitskaite.

Additional information

Original Russian Text © I.B. Virbitskaite, V.A. Borovlev, L. Popova-Zeugmann, 2016, published in Programmirovanie, 2016, Vol. 42, No. 4.

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Virbitskaite, I.B., Borovlev, V.A. & Popova-Zeugmann, L. “Truly concurrent” and nondeterministic semantics of discrete-time Petri nets. Program Comput Soft 42, 187–197 (2016). https://doi.org/10.1134/S0361768816040071

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  • DOI: https://doi.org/10.1134/S0361768816040071

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