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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 1, Pages 74–87 (Mi ivm6554)  

This article is cited in 5 scientific papers (total in 5 papers)

Almost periodicity, finite automata mappings, and related effectiveness issues

Yu. L. Pritykin

Moscow State University, Moscow, Russia

Abstract: We introduce a class of eventually almost periodic sequences where some suffix is almost periodic (i.e., uniformly recurrent). The class of generalized almost periodic sequences includes the class of eventually almost periodic sequences, and we prove this inclusion to be strict. We also prove that the class of eventually almost periodic sequences is closed under finite automata mappings and finite transductions. Moreover, we obtain an effective form of this result. In conclusion we consider some algorithmic questions related to the almost periodicity.

Keywords: almost periodic sequences, finite automata, effectiveness.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:1, 59–69

Bibliographic databases:

UDC: 519.115+519.713
Received: 08.12.2006

Citation: Yu. L. Pritykin, “Almost periodicity, finite automata mappings, and related effectiveness issues”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 1, 74–87; Russian Math. (Iz. VUZ), 54:1 (2010), 59–69

Citation in format AMSBIB
\Bibitem{Pri10}
\by Yu.~L.~Pritykin
\paper Almost periodicity, finite automata mappings, and related effectiveness issues
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 1
\pages 74--87
\mathnet{http://mi.mathnet.ru/ivm6554}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2664487}
\zmath{https://zbmath.org/?q=an:1184.68329}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 1
\pages 59--69
\crossref{https://doi.org/10.3103/S1066369X1001007X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649581338}


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    This publication is cited in the following articles:
    1. An. A. Muchnik, Yu. L. Pritykin, A. L. Semenov, “Sequences close to periodic”, Russian Math. Surveys, 64:5 (2009), 805–871  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Raskin M.A., “O nizhnei otsenke regulyatora pryamogo proizvedeniya pochti periodicheskoi i periodicheskoi posledovatelnostei”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 6, 7–11  mathscinet  zmath  elib
    3. Durand F., “Decidability of Uniform Recurrence of Morphic Sequences”, Int. J. Found. Comput. Sci., 24:1, SI (2013), 123–146  crossref  mathscinet  zmath  isi  elib  scopus
    4. Alvin L., “Uniformly Recurrent Sequences and Minimal Cantor Omega-Limit Sets”, Fundam. Math., 231:3 (2015), 273–284  crossref  mathscinet  zmath  isi  elib  scopus
    5. N. N. Korneeva, “Automata transformations of prefix decidable and decidable by Buchi superwords”, Russian Math. (Iz. VUZ), 60:7 (2016), 47–55  mathnet  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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