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Definability by Horn formulas and linear time on cellular automata

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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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Dates and versions

hal-01494246 , version 1 (23-03-2017)
hal-01494246 , version 2 (22-09-2017)

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Cite

Nicolas Bacquey, Etienne Grandjean, Frédéric Olive. Definability by Horn formulas and linear time on cellular automata. 2017. ⟨hal-01494246v1⟩
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