Turing-completeness of asynchronous non-camouflage cellular automata

Tatsuya Yamashita, Teijiro Isokawa, Ferdinand Peper, Ibuki Kawamata, Masami Hagiya

Research output: Contribution to journalArticle

Abstract

Asynchronous Boolean totalistic cellular automata have recently attracted attention as promising models for implementation by reaction-diffusion systems. It is unknown, however, to what extent they are able to conduct computation. In this paper, we introduce the so-called non-camouflage property, which means that a cell's update is insensitive to neighboring states that equal its own state. This property subsumes the Boolean totalistic property, which signifies the existence of states in a cell's neighborhood, but is not concerned with how many cells are in those states. We argue that the non-camouflage property is extremely useful for the implementation of reaction-diffusion systems, and we construct an asynchronous cellular automaton with this property that is Turing-complete by directly simulating Turing machines. We also construct another asynchronous cellular automaton, but this model incorporates the so-called freezing property [1], which restricts the direction of transitions of each cell to one-way. We show that this model is Turing-complete, since it can simulate the temporal evolution of elementary cellular automata. These results indicate the feasibility of computation by reaction-diffusion systems.

Original languageEnglish
Article number104539
JournalInformation and Computation
Volume274
DOIs
Publication statusPublished - 2020 Oct

Keywords

  • Asynchronous cellular automata
  • Boolean totalistic
  • Elementary cellular automata
  • Freezing
  • Non-camouflage
  • Turing machine

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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