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arXiv · 1907.04211

Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour

Sergio J. Martinez·Ivan M. Mendoza·Genaro J. Martinez·Shigeru Ninagawa
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Abstract

Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.

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Sergio J. Martinez, Ivan M. Mendoza, Genaro J. Martinez, Shigeru Ninagawa. 2019-07-06. Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour. https://arxiv.org/abs/1907.04211

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