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Algebraic Analysis of the Computation in the Belousov-Zhabotinksy Reaction

Submitted by tim.davies on Wed, 07/03/2012 - 14:21
TitleAlgebraic Analysis of the Computation in the Belousov-Zhabotinksy Reaction
Publication TypeConference Paper
Year of Publication2012
AuthorsDini, P, Nehaniv, CL, Egri-Nagy, A, Schilstra, MJ
Date Published01/2012
Keywordsalgebra, computer science
AbstractWe 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 di erent simple non-abelian groups (SNAGs), the largest of which is A9. Although the precise computational signi cance 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.
Files: 
ipcat2012_Short_Paper.pdf