A classification of one-dimensional cellular automata using infinite computations

D’Alotto, Louis

Applied Mathematics and Computation, 2015, vol. 255, issue C, 15-24

Abstract: This paper proposes an application of the Infinite Unit Axiom and grossone, introduced by Yaroslav Sergeyev (see Sergeyev (2003, 2009, 2013, 2008, 2008) [15–19]), to classify one-dimensional cellular automata whereby each class corresponds to a different and distinct dynamical behavior. The forward dynamics of a cellular automaton map are studied via defined classes. Using these classes, along with the Infinite Unit Axiom and grossone, the number of configurations that equal those of a given configuration, in some finite central window, under an automaton map can now be computed. Hence a classification scheme for one-dimensional cellular automata is developed, whereby determination in a particular class is dependent on the number of elements in their respective forward iteration classes.

Keywords: Cellular automata; Infinite Unit Axiom; Grossone; Metric; Dynamical systems (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:255:y:2015:i:c:p:15-24

DOI: 10.1016/j.amc.2014.06.087

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