On the complexity of the stability problem of binary freezing totalistic cellular automata
Goles
E
author
Maldonado
D
author
Montealegre
P
author
Ollinger
N
author
2020
English
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. (C) 2020 Elsevier Inc. All rights reserved.
Cellular automata
Computational complexity
Freezing cellular automata
Totalistic cellular automata
Fast parallel algorithms
P-Complete
WOS:000573267700008
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text
10.1016/j.ic.2020.104535
Goles_etal2020
Information And Computation
Inf. Comput.
2020
Academic Press Inc Elsevier Science
continuing
periodical
academic journal
274
21 pp
0890-5401