Global properties of 2D cellular automata: some complexity results
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.
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