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Step Semantics of Boolean Nets

Lookup NU author(s): Professor Maciej Koutny, Dr Marta Koutny

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Abstract

Boolean nets - such as elementary net systems - 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.


Publication metadata

Author(s): Pietkiewicz-Koutny M; Koutny M; Kleijn J; Rozenberg G

Publication type: Report

Series Title: School of Computing Science Technical Report Series

Year: 2011

Pages: 24

Source Publication Date: November 2011

Report Number: 1298

Institution: School of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne


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