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Universality Frontier for Asynchronous Cellular Automata

Authors Ivan Baburin , Matthew Cook, Florian Grötschla, Andreas Plesner , Roger Wattenhofer

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  • Theory of computation → Models of computation
Keywords
  • Universality
  • Asynchronous Cellular Automata
  • Automata Networks

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Abstract

In this work, we investigate computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous update schedule. We introduce flip automata networks (FANs), a simple modification of automata networks that remain robust under any asynchronous updating order. By using FANs as a middleman, we show that asynchronous automata can efficiently simulate their synchronous counterparts with a linear memory overhead, which improves upon the previously established quadratic bound. Additionally, we address the universality gap for (a)synchronous cellular automata-the boundary separating universal and non-universal automata, which is still not fully understood. We tighten this boundary by proving that all one-way asynchronous automata lack universal computational power. Conversely, we establish the existence of a universal asynchronous 6-state first-neighbor automaton in one dimension and a 3-state von Neumann automaton in two dimensions, which represent the smallest known universal constructions to date.

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Ivan Baburin, Matthew Cook, Florian Grötschla, Andreas Plesner, and Roger Wattenhofer. Universality Frontier for Asynchronous Cellular Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.11

Author Details

Ivan Baburin
  • Department of Computer Science, ETH Zürich, Switzerland
Matthew Cook
  • Faculty of Science and Engineering, University of Groningen, The Netherlands
Florian Grötschla
  • Department of Electrical Engineering, ETH Zürich, Switzerland
Andreas Plesner
  • Department of Electrical Engineering, ETH Zürich, Switzerland
Roger Wattenhofer
  • Department of Electrical Engineering, ETH Zürich, Switzerland

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