Rice’s Theorem for Generic Limit Sets of Cellular Automata

Author Martin Delacourt

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Martin Delacourt
  • Université d'Orléans, LIFO EA4022, FR-45067 Orléans, France

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Martin Delacourt. Rice’s Theorem for Generic Limit Sets of Cellular Automata. 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. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


The generic limit set of a cellular automaton is a topologically defined set of configurations that intends to capture the asymptotic behaviours while avoiding atypical ones. It was defined by Milnor then studied by Djenaoui and Guillon first, and by Törmä later. They gave properties of this set related to the dynamics of the cellular automaton, and the maximal complexity of its language. In this paper, we prove that every non trivial property of these generic limit sets of cellular automata is undecidable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • cellular automata
  • dynamical systems
  • generic-limit sets
  • Rice’s theorem
  • subshifts


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