Definability by Horn formulas and linear time on cellular automata

Nicolas Bacquey 1, 2 Etienne Grandjean 3 Frédéric Olive 4
2 LINKS - Linking Dynamic Data
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 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 : Thursday, March 23, 2017 - 9:09:03 AM
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Nicolas Bacquey, Etienne Grandjean, Frédéric Olive. Definability by Horn formulas and linear time on cellular automata. 2017. ⟨hal-01494246v1⟩

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