Definability by Horn formulas and linear time on cellular automata

Nicolas Bacquey 1 Etienne Grandjean 2 Frédéric Olive 3
1 LINKS - Linking Dynamic Data
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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.
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01494246
Contributor : Nicolas Bacquey <>
Submitted on : Friday, September 22, 2017 - 4:23:07 PM
Last modification on : Tuesday, April 2, 2019 - 1:35:48 AM
Long-term archiving on : Saturday, December 23, 2017 - 1:56:15 PM

File

0.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

1392

Files downloads

97