Abstract
This paper deals with descriptive complexity of picture languages of any dimension by fragments of existential second-order logic:1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order logic.2) We state natural logical characterizations of the class of picture languages of any dimension d≥1 recognized in linear time on nondeterministic cellular automata, a robust complexity class that contains, for d=1, all the natural NP-complete problems.Our characterizations are essentially deduced from normalization results for first-order and existential second-order logics over pictures.
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