A portfolio of classification problems by one-dimensional cellular automata, over cyclic binary configurations and parallel update

Marco Montalva-Medel, Pedro P.B. de Oliveira, Eric Goles

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Decision problems addressed by cellular automata have been historically expressed either as determining whether initial configurations would belong to a given language, or as classifying the initial configurations according to a property in them. Unlike traditional approaches in language recognition, classification problems have typically relied upon cyclic configurations and fully paralell (two-way) update of the cells, which render the action of the cellular automaton relatively less controllable and difficult to analyse. Although the notion of cyclic languages have been studied in the wider realm of formal languages, only recently a more systematic attempt has come into play in respect to cellular automata with fully parallel update. With the goal of contributing to this effort, we propose a unified definition of classification problem for one-dimensional, binary cellular automata, from which various known problems are couched in and novel ones are defined, and analyse the solvability of the new problems. Such a unified perspective aims at increasing existing knowledge about classification problems by cellular automata over cyclic configurations and parallel update.

Original languageEnglish
Pages (from-to)663-671
Number of pages9
JournalNatural Computing
Volume17
Issue number3
DOIs
StatePublished - 1 Sep 2018

Keywords

  • Classification problem
  • Decision problem
  • Density
  • Emergent computation
  • Language recognition
  • One-dimensional cellular automata
  • Parity

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