Dini, Paolo, Nehaniv, Chrystopher L., Egri-Nagy, Attila and Schilstra, Maria J.
Algebraic analysis of the computation in the Belousov-Zhabotinksy reaction.
In: Lones, Michael A., Smith, Stephen L., Teichmann, Sarah, Naef, Felix, Walker, James A. and Trefzer, Martin A., (eds.)
Information Processing in Cells and Tissues: 9th International Conference, Ipcat 2012, Cambridge, Uk, March 31 – April 2, 2012:.
Lecture notes in computer science(7223).
Springer, pp. 216-224.
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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