Acta Informatica

, Volume 50, Issue 1, pp 15–39 | Cite as

Step semantics of boolean nets

  • Jetty Kleijn
  • Maciej Koutny
  • Marta Pietkiewicz-Koutny
  • Grzegorz Rozenberg
Original Article


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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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Jetty Kleijn
    • 1
  • Maciej Koutny
    • 2
  • Marta Pietkiewicz-Koutny
    • 2
  • Grzegorz Rozenberg
    • 1
    • 3
  1. 1.LIACSLeiden University LeidenThe Netherlands
  2. 2.School of Computing ScienceNewcastle UniversityNewcastle upon TyneUK
  3. 3.Department of Computer ScienceUniversity of Colorado at Boulder430 UCB BoulderUSA

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