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Classifying Boolean Nets for Region-based Synthesis

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



Reaction systems are a formal frameworkfor the investigationof processes carried by biochemical reactions.Recently, we investigated ways of modelling reaction systemswithin the domain of Petri nets. This has led to theintroduction a new class of Petri nets, called set-nets,which provide a faithful and elegant computationalmodel matching very closely that exhibited by reaction systems.The key difference between standard Petri nets and set-nets is thatthe former support multiset-based token arithmetic, whereas the lattersupport set-based (or Boolean) operations on tokens.In this paper, we investigate the synthesis problem for set-nets.We do so by showing that the new kind of nets can be treatedwithin the general theory of net synthesis. We also use this as anopportunity to classify a full variety of Boolean nets, generalisingset-nets and their Boolean operations on tokens.We add to the existing theory of net synthesis a detailed studyof connection monoids for Boolean nets which allow us tocapture not only the step semantics of nets but also structural conflictsbetween transitions in Boolean nets.

Publication metadata

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

Editor(s): Desel, J., Yakovlev, A.

Publication type: Conference Proceedings (inc. Abstract)

Conference Name: ART-2011, Applications of Region Theory

Year of Conference: 2011

Pages: 5-21

Publisher: CEUR-WS, RWTH Aachen University

Series Title: CEUR Workshop Proceedings