Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Commutative automata networks

Abstract : Automata networks are mappings of the form f : Q Z → Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its state according to its local function fi : Q Z → Q. One major question is to study the behaviour of a given automata networks under different update schedules. In this paper, we study automata networks that are invariant under many different update schedules. This gives rise to two definitions, locally commutative and globally commu-tative networks. We investigate the relation between commutativity and different forms of locality of update functions; one main conclusion is that globally commutative networks have strong dynamical properties, while locally commutative networks are much less constrained. We also give a complete classification of all globally commutative Boolean networks.
Complete list of metadatas

Cited literature [4 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02548573
Contributor : Guillaume Theyssier <>
Submitted on : Monday, April 20, 2020 - 5:32:39 PM
Last modification on : Wednesday, April 22, 2020 - 1:44:33 AM

Files

commuting_networks.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02548573, version 1
  • ARXIV : 2004.09806

Citation

Florian Bridoux, Maximilien Gadouleau, Guillaume Theyssier. Commutative automata networks. 2020. ⟨hal-02548573⟩

Share

Metrics

Record views

49

Files downloads

12