LIPIcs.STACS.2010.2474.pdf
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Revisiting the Rice Theorem of Cellular Automata
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27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2010-03-09
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Pierre Guillon and Gaétan Richard. Revisiting the Rice Theorem of Cellular Automata. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 441-452, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2474
https://doi.org/10.4230/LIPIcs.STACS.2010.2474
Abstract
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, \ie the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution.
In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical ``Rice Theorem'' that Kari proved on cellular automata with arbitrary state sets.
Keywords
- Cellular automata
- undecidability
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