A classification of one-dimensional cellular automata using infinite computations

摘要

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.