On the complexity of the stability problem of binary freezing totalistic cellular automata

Eric Goles, Diego Maldonado, Pedro Montealegre, Nicolas Ollinger

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

3 Citas (Scopus)

Resumen

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors. We classify all the Cellular Automata in the class of TFCA, grouping them in five different classes: the Trivial rules, Turing Universal rules, Algebraic rules, Topological rules and Fractal Growing rules. At the same time, we study in this family the STABILITY problem, consisting in deciding whether an inactive cell becomes active, given an initial configuration. We exploit the properties of the automata in each group to show that: • For Algebraic and Topological Rules the STABILITY problem is in NC. • For Turing Universal rules the STABILITY problem is P-Complete.

Idioma originalInglés
Número de artículo104535
PublicaciónInformation and Computation
Volumen274
DOI
EstadoPublicada - oct. 2020

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