License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.AUTOMATA.2021.1
URN: urn:nbn:de:0030-drops-140105
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14010/
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Gadouleau, Maximilien

Dynamical Properties of Disjunctive Boolean Networks (Invited Talk)

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OASIcs-AUTOMATA-2021-1.pdf (0.6 MB)

Abstract

A Boolean network is a mapping f :{0,1}ⁿ → {0,1}ⁿ, which can be used to model networks of n interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current configuration of states. In this paper, we are interested in disjunctive networks, where each local function is simply the disjunction of a set of variables. As such, this network is somewhat homogeneous, though the number of variables may vary from entity to entity, thus yielding a generalised cellular automaton. The aim of this paper is to review some of the main results, derive some additional fundamental results, and highlight some open problems on the dynamics of disjunctive networks. We first review the different defining characteristics of disjunctive networks and several ways of representing them using graphs, Boolean matrices, or binary relations. We then focus on three dynamical properties of disjunctive networks: their image points, their periodic points, and their fixed points. For each class of points, we review how they can be characterised and study how many they could be. The paper finishes with different avenues for future work on the dynamics of disjunctive networks and how to generalise them.

BibTeX - Entry

@InProceedings{gadouleau:OASIcs.AUTOMATA.2021.1,
  author =	{Gadouleau, Maximilien},
  title =	{{Dynamical Properties of Disjunctive Boolean Networks}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{1:1--1:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14010},
  URN =		{urn:nbn:de:0030-drops-140105},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.1},
  annote =	{Keywords: Boolean networks, disjunction, conjunction, fixed points, rank}
}

Keywords: Boolean networks, disjunction, conjunction, fixed points, rank
Collection: 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)
Issue Date: 2021
Date of publication: 28.06.2021

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