Algebraic Analysis of the Computation in the Belousov-Zhabotinksy Reaction
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- Dini P., Nehaniv C.L., Egri-Nagy A., Schilstra M.J. (2012) Algebraic Analysis of the Computation in the Belousov-Zhabotinksy Reaction. In: Lones M.A., Smith S.L., Teichmann S., Naef F., Walker J.A., Trefzer M.A. (eds) Information Processign in Cells and Tissues. IPCAT 2012. Lecture Notes in Computer Science, vol 7223. Springer, Berlin, Heidelberg
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 A9. 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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