@inproceedings{e248ef4bd0644eb3acf8e5d57ac1c0e8,

title = "Algebraic analysis of the computation in the Belousov-Zhabotinsky reaction",

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 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.",

author = "P. Dini and C.L. Nehaniv and A. Egri-Nagy and M. Schilstra",

year = "2012",

doi = "10.1007/978-3-642-28792-3_27",

language = "English",

isbn = "9783642287916",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature",

pages = "216--224",

booktitle = "Information Processing in Cells and Tissues",

address = "Netherlands",

note = "IPCAT 2012 ; Conference date: 31-03-2012",

}