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Universal One-dimensional Cellular Automata Derived from Turing Machines
Sergio J. Martínez, Iván M. Mendoza, Genaro J. Martínez and Shigeru Ninagawa

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.

Keywords: Turing machines, cellular automata, spatial dynamics, universality

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