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Documents authored by Sené, Sylvain

Document
DOI: 10.4230/LIPIcs.SAND.2024.19
Complexity of Boolean Automata Networks Under Block-Parallel Update Modes

Authors: Kévin Perrot, Sylvain Sené, and Léah Tapin

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

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.
Cite as

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)

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@InProceedings{perrot_et_al:LIPIcs.SAND.2024.19,
  author =	{Perrot, K\'{e}vin and Sen\'{e}, Sylvain and Tapin, L\'{e}ah},
  title =	{{Complexity of Boolean Automata Networks Under Block-Parallel Update Modes}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.19},
  URN =		{urn:nbn:de:0030-drops-198973},
  doi =		{10.4230/LIPIcs.SAND.2024.19},
  annote =	{Keywords: Boolean networks, finite dynamical systems, block-parallel update schedule}
}
Document
DOI: 10.4230/OASIcs.AUTOMATA.2021.10
Non-Deterministic Updates of Boolean Networks

Authors: Loïc Paulevé and Sylvain Sené

Published in: OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)

Abstract
Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network evolves over time. Many of updating modes from the literature, including synchronous and asynchronous modes, can be defined as the composition of elementary deterministic configuration updates, i.e., by functions mapping configurations of the network. Nevertheless, alternative dynamics have been introduced using ad-hoc auxiliary objects, such as that resulting from binary projections of Memory Boolean networks, or that resulting from additional pseudo-states for Most Permissive Boolean networks. One may wonder whether these latter dynamics can still be classified as updating modes of finite Boolean networks, or belong to a different class of dynamical systems. In this paper, we study the extension of updating modes to the composition of non-deterministic updates, i.e., mapping sets of finite configurations. We show that the above dynamics can be expressed in this framework, enabling a better understanding of them as updating modes of Boolean networks. More generally, we argue that non-deterministic updates pave the way to a unifying framework for expressing complex updating modes, some of them enabling transitions that cannot be computed with elementary and non-elementary deterministic updates.
Cite as

Loïc Paulevé and Sylvain Sené. Non-Deterministic Updates of Boolean Networks. In 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{pauleve_et_al:OASIcs.AUTOMATA.2021.10,
  author =	{Paulev\'{e}, Lo\"{i}c and Sen\'{e}, Sylvain},
  title =	{{Non-Deterministic Updates of Boolean Networks}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{10:1--10:16},
  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/entities/document/10.4230/OASIcs.AUTOMATA.2021.10},
  URN =		{urn:nbn:de:0030-drops-140196},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.10},
  annote =	{Keywords: Natural computing, discrete dynamical systems, semantics}
}
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