University of Hertfordshire

By the same authors

Algebraic analysis of the computation in the Belousov-Zhabotinsky reaction

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

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Original languageEnglish
Title of host publicationInformation Processing in Cells and Tissues
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
CountryUnited Kingdom
Period31/03/12 → …


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.

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