| GREYC - AMACC group | Algorithms, Computational Models, Alea, Cryptography, Complexity |  |
Conference papers
Definability by Horn formulas and linear time on cellular automata
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.
Cited literature [20 references]
https://hal.archives-ouvertes.fr/hal-01494246
Contributor : Nicolas Bacquey <>
Submitted on : Friday, September 22, 2017 - 4:23:07 PM
Last modification on : Friday, December 11, 2020 - 6:44:06 PM
Long-term archiving on: : Saturday, December 23, 2017 - 1:56:15 PM
Contributor : Nicolas Bacquey <>
Submitted on : Friday, September 22, 2017 - 4:23:07 PM
Last modification on : Friday, December 11, 2020 - 6:44:06 PM
Long-term archiving on: : Saturday, December 23, 2017 - 1:56:15 PM
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