Inversion 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, 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. We then present a transformation of problems concerning tilings into problems concerning cellular automata. Keywords: cellular automata, inversion, reversibility, complexity R'esum'e Nous prouvons dans cet article la co-NP-compl'etude du probl `eme de d'ecision suivant: "'etant donn'e un automate cellulaire plan A, sa restriction aux configurations finies de taille inf'erieure `a la taille du codage de A est-elle bijective ?" Nous introduisons deux probl`emes de d'ecision concernant les machines de Turing et les pavages, puis nous d'emontrons que ces probl`emes sont NP-complets. Pour prouver notre r'esultat principal, ..