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Step semantics of boolean nets

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Abstract

Boolean nets are a family of Petri net models with very simple markings which are sets of places. We investigate several classes of boolean nets distinguished by different kinds of individual connections between places and transitions, as well as different ways in which these connections are combined in order to specify the effect of executing steps of transitions. The latter aspect can be captured by connection monoids. A key advantage of using connection monoids is that by describing the step semantics of a class of Petri nets in terms of a connection monoid, one can apply results developed within a general theory of Petri net synthesis. In this paper, we provide an extensive classification of boolean nets which can be described by connection monoids. This classification is based on the realisation that the different ways of interpreting combinations of connections can be made explicit using a higher level monoid. Moreover, we demonstrate that connection monoids can capture other behavioural properties of boolean nets, such as structural conflicts between transitions.

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Notes

  1. In [13] boolean nets are a simple class of coloured nets for the modeling of control flow; tokens have colour ‘true’ or ‘false’ and the guards are formulas from propositional logic.

  2. By connection patterns we mean sub-graphs corresponding to specific connections appearing in net-type graphs of boolean nets.

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Acknowledgments

We are grateful to the anonymous reviewers for constructive comments and suggestions. This research was supported by the Pascal Chair award from Leiden University, the Epsrc Verdad and Gaels projects, and Nsfc Grants 60910004 and 61133001.

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Authors and Affiliations

  1. LIACS, Leiden University, P.O. Box 9512, 2300 RA,  Leiden, The Netherlands

    Jetty Kleijn & Grzegorz Rozenberg

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

    Maciej Koutny & Marta Pietkiewicz-Koutny

  3. Department of Computer Science, University of Colorado at Boulder, 430 UCB Boulder, CO,  80309-0430, USA

    Grzegorz Rozenberg

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  1. Jetty Kleijn
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  2. Maciej Koutny
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  3. Marta Pietkiewicz-Koutny
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  4. Grzegorz Rozenberg
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Correspondence to Jetty Kleijn.

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Kleijn, J., Koutny, M., Pietkiewicz-Koutny, M. et al. Step semantics of boolean nets. Acta Informatica 50, 15–39 (2013). https://doi.org/10.1007/s00236-012-0170-2

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