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Mat. Zametki, 2006, Volume 80, Issue 5, Pages 751–756 (Mi mz3084)  

This article is cited in 6 scientific papers (total in 6 papers)

Finite-automaton transformations of strictly almost-periodic sequences

Yu. L. Pritykin

M. V. Lomonosov Moscow State University

Abstract: Different versions of the notion of almost-periodicity are natural generalizations of the notion of periodicity. The notion of strict almost-periodicity appeared in symbolic dynamics, but later proved to be fruitful in mathematical logic and the theory of algorithms as well. In the paper, a class of essentially almost-periodic sequences (i.e., strictly almost-periodic sequences with an arbitrary prefix added at the beginning) is considered. It is proved that the property of essential almost-periodicity is preserved under finite-automaton transformations, as well as under the action of finite transducers. The class of essentially almost-periodic sequences is contained in the class of almost-periodic sequences. It is proved that this inclusion is strict.

DOI: https://doi.org/10.4213/mzm3084

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English version:
Mathematical Notes, 2006, 80:5, 710–714

Bibliographic databases:

UDC: 519.115.8+519.713
Received: 27.06.2005

Citation: Yu. L. Pritykin, “Finite-automaton transformations of strictly almost-periodic sequences”, Mat. Zametki, 80:5 (2006), 751–756; Math. Notes, 80:5 (2006), 710–714

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pritykin Yu., “On Almost Periodicity Criteria for Morphic Sequences in Some Particular Cases”, Developments in Language Theory, Proceedings, Lecture Notes in Computer Science, 4588, eds. Harju T., Karhumaki J., Lepisto A., Springer-Verlag Berlin, 2007, 361–370  crossref  mathscinet  zmath  isi
    2. 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
    3. Nicolas F., Pritykin Yu., “On uniformly recurrent morphic sequences”, Internat. J. Found. Comput. Sci., 20:5 (2009), 919–940  crossref  mathscinet  zmath  isi  elib  scopus
    4. Yu. L. Pritykin, “Almost periodicity, finite automata mappings, and related effectiveness issues”, Russian Math. (Iz. VUZ), 54:1 (2010), 59–69  mathnet  crossref  mathscinet  zmath
    5. 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
    6. 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
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