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Definability by Horn formulas and linear time on cellular automata

Nicolas Bacquey 1 Etienne Grandjean 2 Frédéric Olive 3
1 LINKS - Linking Dynamic Data
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189, Inria Lille - Nord Europe
2 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : We establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d + 1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time.
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Submitted on : Friday, September 22, 2017 - 4:23:07 PM
Last modification on : Friday, December 11, 2020 - 6:44:06 PM
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Nicolas Bacquey, Etienne Grandjean, Frédéric Olive. Definability by Horn formulas and linear time on cellular automata. ICALP 2017 - 44th International Colloquium on Automata, Languages and Programming, Jul 2017, Warsaw, Poland. pp.1-14, ⟨10.4230/LIPIcs.ICALP.2017.99⟩. ⟨hal-01494246v2⟩



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