License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.AUTOMATA.2021.8
URN: urn:nbn:de:0030-drops-140170
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14017/
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Grente, Théo ; Grandjean, Étienne

Conjunctive Grammars, Cellular Automata and Logic

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OASIcs-AUTOMATA-2021-8.pdf (0.8 MB)

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-dimensional one-way cellular automata. We prove two weakened versions of the open question Conj ⊆? RealTime1CA, where RealTime1CA is the class of languages recognized by real-time one-dimensional two-way cellular automata:
1) it is true for unary languages;
2) Conj ⊆ RealTime2OCA, i.e. any conjunctive language is recognized by a real-time two-dimensional one-way cellular automaton. Interestingly, we express the rules of a conjunctive grammar in two Horn logics, which exactly characterize the complexity classes RealTime1CA and RealTime2OCA.

BibTeX - Entry

@InProceedings{grente_et_al:OASIcs.AUTOMATA.2021.8,
  author =	{Grente, Th\'{e}o and Grandjean, \'{E}tienne},
  title =	{{Conjunctive Grammars, Cellular Automata and Logic}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{8:1--8:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14017},
  URN =		{urn:nbn:de:0030-drops-140170},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.8},
  annote =	{Keywords: Computational complexity, Real-time, One-dimensional/two-dimensional cellular automaton, One-way/two-way communication, Grid-circuit, Unary language, Descriptive complexity, Existential second-order logic, Horn formula}
}

Keywords: Computational complexity, Real-time, One-dimensional/two-dimensional cellular automaton, One-way/two-way communication, Grid-circuit, Unary language, Descriptive complexity, Existential second-order logic, Horn formula
Collection: 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)
Issue Date: 2021
Date of publication: 28.06.2021

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