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DOI: 10.4230/LIPIcs.STACS.2010.2474
URN: urn:nbn:de:0030-drops-24744
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Guillon, Pierre ; Richard, GaƩtan

Revisiting the Rice Theorem of Cellular Automata

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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.

BibTeX - Entry

  author =	{Pierre Guillon and Ga{\'e}tan Richard},
  title =	{{Revisiting the Rice Theorem of Cellular Automata}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{441--452},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-24744},
  doi =		{10.4230/LIPIcs.STACS.2010.2474},
  annote =	{Keywords: Cellular automata, undecidability}

Keywords: Cellular automata, undecidability
Collection: 27th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2010
Date of publication: 09.03.2010

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