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URN: urn:nbn:de:0030-drops-69780
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On the Synchronisation Problem over Cellular Automata

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Abstract

Cellular automata are a discrete, synchronous, and uniform dynamical system that give rise to a wide range of dynamical behaviours. In this paper, we investigate whether this system can achieve synchronisation. We study the cases of classical bi-infinite configurations, periodic configurations, and periodic configurations of prime period. In the two former cases, we prove that only a "degenerated" form of synchronisation - there exists a fix-point - is possible. In the latter case, we give an explicit construction of a cellular automaton for which any periodic configuration of prime period eventually converges to cycle of two uniform configurations. Our construction is based upon sophisticated tools: aperiodic NW-deterministic tilings and partitioned intervals.

BibTeX - Entry

@InProceedings{richard:LIPIcs:2017:6978,
  author =	{Ga{\'e}tan Richard},
  title =	{{On the Synchronisation Problem over Cellular Automata}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{54:1--54:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte Vallée},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6978},
  URN =		{urn:nbn:de:0030-drops-69780},
  doi =		{10.4230/LIPIcs.STACS.2017.54},
  annote =	{Keywords: cellular automata, dynamical systems, aperiodic tiling, synchronisation}
}

Keywords: cellular automata, dynamical systems, aperiodic tiling, synchronisation
Seminar: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue date: 2017
Date of publication: 2017


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