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Algebraic analysis of the computation in the Belousov-Zhabotinksy reaction

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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 9. 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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en

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application/pdf

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http://eprints.lse.ac.uk/43167/1/Algebraic%20analysis%20of%20the%20computation%20in%20the%20Belousov-Zhabotinsky%20reaction%20%28lsero%29.pdf

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