On the computational power of totalistic cellular automata

Dan Gordon

doi:10.1007/BF01692058

On the computational power of totalistic cellular automata

Dan Gordon

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Totalistic cellular automata, introduced by S. Wolfram, are cellular automata in which the state transition function depends only on the sum of the states in a cell's neighborhood. Each state is considered as a nonnegative integer and the sum includes the cell's own state. It is shown that one-dimensional totalistic cellular automata can simulate an arbitrary Turing machine in linear time, even when the neighborhood is restricted to one cell on each side. This result settles Wolfram's conjecture that totalistic cellular automata are computation-universal.

Original language	English
Pages (from-to)	43-52
Number of pages	10
Journal	Mathematical Systems Theory
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/BF01692058
State	Published - Dec 1987

ASJC Scopus subject areas

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics

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10.1007/BF01692058

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On the computational power of totalistic cellular automata

Abstract

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