In this paper, we prove the co-NP-completeness of the following decision problem: “given a 2-dimensional cellular automaton A (even with Von Neumann neighborhood), is A injective when restricted to finite configurations not greater than its length?” In order to prove this result, we introduce two decision problems concerning respectively Turing Machines and tilings that we prove NP-complete. Then, we transform problems concerning tilings into problems concerning cellular automata.
CITATION STYLE
Durand, B. (1993). Global properties of 2D cellular automata: Some complexity results. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 711 LNCS, pp. 433–441). Springer Verlag. https://doi.org/10.1007/3-540-57182-5_35
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