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Conjunctive grammars, cellular automata and logic

Théo Grente 1 Etienne Grandjean 1
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : The expressive power of the class Conj of conjunctive languages, i.e. languages generated by the conjunctive grammars of Okhotin, is largely unknown, while its restriction LinConj to linear conjunctive grammars equals the class of languages recognized by real-time one-way one-dimensional cellular automata. We prove two weakened versions of the open question Conj ⊆? RealTimeCA: 1) it is true for unary languages; 2) Conj ⊆ RealTime2OCA, i.e. any conjunctive language is recognized by a real-time one-way two-dimensional cellular automaton. Interestingly, we express the rules of a conjunctive grammar in two Horn logics, which exactly characterize the complexity classes RealTimeCA and RealTime2OCA.
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https://hal.archives-ouvertes.fr/hal-03167529
Contributor : Théo Grente <>
Submitted on : Friday, March 12, 2021 - 10:45:27 AM
Last modification on : Tuesday, March 16, 2021 - 3:27:57 AM
Long-term archiving on: : Sunday, June 13, 2021 - 6:31:20 PM

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Théo Grente, Etienne Grandjean. Conjunctive grammars, cellular automata and logic. 2021. ⟨hal-03167529⟩

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