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 . 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.
|Title of host publication||Information Processing in Cells and Tissues|
|Number of pages||9|
|Publication status||Published - 2012|
|Event||IPCAT 2012 - Cambridge, United Kingdom|
Duration: 31 Mar 2012 → …
|Name||Lecture Notes in Computer Science|
|Period||31/03/12 → …|