Formal Languages over GF(2)

Ekaterina Bakinova, Artem Basharin, Igor Batmanov, Konstantin Lyubort, Alexander Okhotin, Elizaveta Sazhneva

Research outputpeer-review

5 Citations (Scopus)

Abstract

Variants of the union and concatenation operations on formal languages are investigated, in which Boolean logic in the definitions (that is, conjunction and disjunction) is replaced with the operations in the two-element field GF(2) (conjunction and exclusive OR). Union is thus replaced with symmetric difference, whereas concatenation gives rise to a new GF(2)-concatenation operation, which is notable for being invertible. All operations preserve regularity, and their state complexity is determined. Next, a new class of formal grammars based on GF(2)-operations is defined, and it is shown to have the same computational complexity as ordinary grammars with union and concatenation.

Original languageEnglish
Title of host publicationLanguage and Automata Theory and Applications - 12th International Conference, LATA 2018, Proceedings
PublisherSpringer
Pages68-79
Number of pages12
ISBN (Print)9783319773124
DOIs
Publication statusPublished - 1 Jan 2018
Event12th International Conference on Language and Automata Theory and Applications, LATA 2018 - Ramat Gan
Duration: 9 Apr 201811 Apr 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10792 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Conference on Language and Automata Theory and Applications, LATA 2018
CountryIsrael
CityRamat Gan
Period9/04/1811/04/18

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Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bakinova, E., Basharin, A., Batmanov, I., Lyubort, K., Okhotin, A., & Sazhneva, E. (2018). Formal Languages over GF(2). In Language and Automata Theory and Applications - 12th International Conference, LATA 2018, Proceedings (pp. 68-79). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10792 LNCS). Springer. https://doi.org/10.1007/978-3-319-77313-1_5