Algebraic Analysis of the Computation in the Belousov-Zhabotinksy Reaction

  • Paolo Dini
  • Chrystopher L. Nehaniv
  • Attila Egri-Nagy
  • Maria J. Schilstra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7223)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paolo Dini
    • 1
    • 2
  • Chrystopher L. Nehaniv
    • 1
  • Attila Egri-Nagy
    • 1
    • 3
  • Maria J. Schilstra
    • 1
  1. 1.Royal Society Wolfson BioComputation Research Lab, Centre for Computer Science and Informatics ResearchUniversity of HertfordshireUnited Kingdom
  2. 2.Department of Media and CommunicationsLondon School of Economics and Political ScienceLondonUnited Kingdom
  3. 3.School of Computing and MathematicsUniversity of Western SydneyParramattaAustralia

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