Recurrence in Multidimensional Words

Émilie Charlier, Svetlana Puzynina, Élise Vandomme

Research output

1 Citation (Scopus)

Abstract

In this paper we study various modifications of the notion of uniform recurrence in multidimensional infinite words. A d-dimensional infinite word is said to be uniformly recurrent if for each (Formula Presented) there exists (Formula Presented) such that each block of size (Formula Presented) contains the prefix of size (Formula Presented). We introduce and study a new notion of uniform recurrence of multidimensional infinite words: for each rational slope (Formula Presented), each rectangular prefix must occur along this slope, that is in positions (Formula Presented), with bounded gaps. Such words are called uniformly recurrent along all directions. We provide several constructions of multidimensional infinite words satisfying this condition, and more generally, a series of three conditions on recurrence. We study general properties of these new notions and in particular we study the strong uniform recurrence of fixed points of square morphisms.

Original languageEnglish
Title of host publicationLanguage and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings
EditorsDana Shapira, Alexander Okhotin, Carlos Martín-Vide
PublisherSpringer
Pages397-408
Number of pages12
ISBN (Print)9783030134341
DOIs
Publication statusPublished - 1 Jan 2019
Event13th International Conference on Language and Automata Theory and Applications, LATA 2019 - St. Petersburg
Duration: 26 Mar 201929 Mar 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11417 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Language and Automata Theory and Applications, LATA 2019
CountryRussian Federation
CitySt. Petersburg
Period26/03/1929/03/19

Fingerprint

Recurrence
Infinite Words
Prefix
Slope
Morphisms
Fixed point
Series

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Charlier, É., Puzynina, S., & Vandomme, É. (2019). Recurrence in Multidimensional Words. In D. Shapira, A. Okhotin, & C. Martín-Vide (Eds.), Language and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings (pp. 397-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11417 LNCS). Springer. https://doi.org/10.1007/978-3-030-13435-8_29
Charlier, Émilie ; Puzynina, Svetlana ; Vandomme, Élise. / Recurrence in Multidimensional Words. Language and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings. editor / Dana Shapira ; Alexander Okhotin ; Carlos Martín-Vide. Springer, 2019. pp. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Charlier, É, Puzynina, S & Vandomme, É 2019, Recurrence in Multidimensional Words. in D Shapira, A Okhotin & C Martín-Vide (eds), Language and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11417 LNCS, Springer, pp. 397-408, St. Petersburg, 26/03/19. https://doi.org/10.1007/978-3-030-13435-8_29

Recurrence in Multidimensional Words. / Charlier, Émilie; Puzynina, Svetlana; Vandomme, Élise.

Language and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings. ed. / Dana Shapira; Alexander Okhotin; Carlos Martín-Vide. Springer, 2019. p. 397-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11417 LNCS).

Research output

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Charlier É, Puzynina S, Vandomme É. Recurrence in Multidimensional Words. In Shapira D, Okhotin A, Martín-Vide C, editors, Language and Automata Theory and Applications - 13th International Conference, LATA 2019, Proceedings. Springer. 2019. p. 397-408. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-13435-8_29