Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour
Cellular Automata and Lattice Gases
2019-07-10 v1 Computation and Language
Data Structures and Algorithms
Logic in Computer Science
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.
Keywords
Cite
@article{arxiv.1907.04211,
title = {Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour},
author = {Sergio J. Martinez and Ivan M. Mendoza and Genaro J. Martinez and Shigeru Ninagawa},
journal= {arXiv preprint arXiv:1907.04211},
year = {2019}
}
Comments
18 pages, 8 tables, 3 figures. https://www.oldcitypublishing.com/journals/ijuc-home/ijuc-issue-contents/ijuc-volume-14-number-2-2019/ijuc-14-2-p-121-138/