License
when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2011.284
URN: urn:nbn:de:0030-drops-30187
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3018/

Fates, Nazim

Stochastic Cellular Automata Solve the Density Classification Problem with an Arbitrary Precision

pdf-format:
Dokument 1.pdf (681 KB)


Abstract

The density classification problem consists in using a binary cellular automaton (CA) to decide whether an initial configuration contains more 0s or 1s. This problem is known for having no exact solution in the case of binary, deterministic, one-dimensional CA. Stochastic cellular automata have been studied as an alternative for solving the problem. This paper is aimed at presenting techniques to analyse the behaviour of stochastic CA rules, seen as a ``blend'' of deterministic CA rules. Using analytical calculations and numerical simulations, we analyse two previously studied rules and present a new rule. We estimate their quality of classification and their average time of classification. We show that the new rule solves the problem with an arbitrary precision. From a practical point of view, this rule is effective and exhibits a high quality of classification, even when the simulation time is kept small.

BibTeX - Entry

@InProceedings{fates:LIPIcs:2011:3018,
  author =	{Nazim Fates},
  title =	{{Stochastic Cellular Automata Solve the Density Classification Problem with an Arbitrary Precision}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{284--295},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3018},
  URN =		{urn:nbn:de:0030-drops-30187},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2011.284},
  annote =	{Keywords: stochastic and probabilistic cellular automata, density classification problem, models of spatially distributed computing, stochastic process}
}

Keywords: stochastic and probabilistic cellular automata, density classification problem, models of spatially distributed computing, stochastic process
Seminar: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue date: 2011
Date of publication: 11.03.2011


DROPS-Home | Fulltext Search | Imprint Published by LZI