Algebraic analysis of the computation in the Belousov-Zhabotinsky reaction

P. Dini, C.L. Nehaniv, A. Egri-Nagy, M. Schilstra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


We analyse two very simple Petri nets inspired by the Oregonator model of the Belousov-Zhabotinsky reaction using our stochastic Petri net simulator. We then perform the Krohn-Rhodes holonomy decomposition of the automata derived from the Petri nets. The simplest case shows that the automaton can be expressed as a cascade of permutation-reset cyclic groups, with only 2 out of the 12 levels having only trivial permutations. The second case leads to a 35-level decomposition with 5 different simple non-abelian groups (SNAGs), the largest of which is A . Although the precise computational significance of these algebraic structures is not clear, the results suggest a correspondence between simple oscillations and cyclic groups, and the presence of SNAGs indicates that even extremely simple chemical systems may contain functionally complete algebras.
Original languageEnglish
Title of host publicationInformation Processing in Cells and Tissues
PublisherSpringer Nature
Number of pages9
ISBN (Electronic)978-3-642-28792-3
ISBN (Print)9783642287916
Publication statusPublished - 2012
EventIPCAT 2012 - Cambridge, United Kingdom
Duration: 31 Mar 2012 → …

Publication series

NameLecture Notes in Computer Science


ConferenceIPCAT 2012
Country/TerritoryUnited Kingdom
Period31/03/12 → …


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