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Complexity of Boolean Automata Networks Under Block-Parallel Update Modes

Authors Kévin Perrot, Sylvain Sené, Léah Tapin

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Kévin Perrot
  • Université publique, Marseille, France
  • Aix-Marseille Univ, CNRS, LIS, Marseille, France
Sylvain Sené
  • Université publique, Marseille, France
  • Aix-Marseille Univ, CNRS, LIS, Marseille, France
Léah Tapin
  • Aix-Marseille Univ, CNRS, LIS, Marseille, France

Acknowledgements

This work received support from ANR-18-CE40-0002 FANs, STIC AmSud CAMA 22-STIC-02 (Campus France MEAE) and HORIZON-MSCA-2022-SE-01-101131549 ACANCOS projects.

Cite AsGet BibTex

Kévin Perrot, Sylvain Sené, and Léah Tapin. Complexity of Boolean Automata Networks Under Block-Parallel Update Modes. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAND.2024.19

Abstract

Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their 0-1 states according to local rules. The dynamics of the network is highly sensitive to update modes, i.e., to the schedule according to which the automata apply their local rule. A new family of update modes appeared recently, called block-parallel, which is dual to the well studied block-sequential. Although basic, it embeds the rich feature of update repetitions among a temporal updating period, allowing for atypical asymptotic behaviors. In this paper, we prove that it is able to breed complex computations, squashing almost all decision problems on the dynamics to the traditionally highest (for reachability questions) class PSPACE. Despite obtaining these complexity bounds for a broad set of local and global properties, we also highlight a surprising gap: bijectivity is still coNP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Boolean networks
  • finite dynamical systems
  • block-parallel update schedule

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