Skip to main content
SpringerLink
Log in

Automata in algebra

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, some algebraic problems are considered. Several aspects of automaton theory and algebraic structures needed to obtain solutions of the problems are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. V. Aleshin, “On bases in automaton substitution groups,” Diskret. Analiz, 17, 111–136 (1970).

    Google Scholar 

  2. S. V. Aleshin, “On non-existence of bases in some classes of initial automata,” Probl. Kibernet, 22, 33–58 (1970).

    Google Scholar 

  3. S. V. Aleshin, “Finite automata and the Burnside problem for periodic semigroups,” Mat. Zametki, 3, 56–78 (1972).

    Google Scholar 

  4. S. V. Aleshin, “On one consequence of the Krohn–Rhodes theorem,” Diskret. Mat., 11, No. 4, 31–37 (1999).

    Google Scholar 

  5. M. A. Arbib, ed., Algebraic Theory of Machines, Languages and Semigroups, Academic Press, New York (1968).

    MATH  Google Scholar 

  6. D. N. Babin, “Completeness of two-place boundedly deterministic functions with respect to superposition,” Diskret. Mat., 1, No. 4, 86–91 (1989).

    MathSciNet  Google Scholar 

  7. A. A. Chasovskikh, “On decidability of the completeness problem for linear automata,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 47–61 (1985).

  8. V. M. Glushkov, “Abstract automaton theory,” Usp. Mat. Nauk, 16, No. 5 (1961).

  9. R. I. Grigorchuk, “On the Milnor problem of group growth,” Dokl. Akad. Nauk SSSR, 271, No. 1, 101–109 (1983).

    MathSciNet  Google Scholar 

  10. M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  11. V. B. Kudryavtsev, S. V. Aleshin, and A. S. Podkolzin, Introduction to Automaton Theory [in Russian], Moscow (1985).

  12. V. V. Makarov, “On automaton permutation groups,” Fundam. Prikl. Mat., 2, No. 1, 171–186 (1996).

    MATH  MathSciNet  Google Scholar 

  13. V. I. Malygin, “Transformation of an automaton group under the action of a feedback operation,” in: VIth All-Union Conf. on Theoretical Problems of Cybernetics (1983).

  14. V. I. Malygin, Algebraic Invariants of Automaton Composition, Ph.D. Thesis (1988).

  15. A. V. Rozhkov, “On the theory of Aleshin-type groups,” Mat. Zametki, 40, No. 5, 572–589 (1986).

    MATH  MathSciNet  Google Scholar 

  16. V. P. Zarovnyj, “Automaton substitutions and group interlacing,” Dokl. Akad. Nauk SSSR, 160, No. 3, 128–144 (1965).

    Google Scholar 

  17. A. Żuk, “Groupes engendr´es par les automates,” Ast´erisque, 317, 141–174 (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    S. V. Aleshin

Authors
  1. S. V. Aleshin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Aleshin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 3, pp. 23–32, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aleshin, S.V. Automata in algebra. J Math Sci 168, 14–20 (2010). https://doi.org/10.1007/s10958-010-9971-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-010-9971-4

Keywords

Search

Navigation