Skip to main content
SpringerLink
Log in

Left-noncounting languages

  • Published:
International Journal of Computer & Information Sciences Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

LetX be a finite alphabet and letX * be the free monoid generated byX. A languageA \( \subseteq \) X * is called left-noncounting if there existsk ≥ 0 such that forx,y εX *,x k y εA if and only ifx k+i y εA. The class of all left-noncounting languages overX forms a Boolean algebra which generally contains properly the class of all noncounting languages overX and is properly contained in the class of all power-separating languages overX. In this paper, we discuss some relations among these three classes of languages and we characterize the automata accepting the left-noncounting languages and the syn tactic monoids of the left-noncounting languages.

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. J. A. Brzozowski, K. Čulik II, and A. Gabrielian, “Classification of noncounting events,”J. Comp. Syst. Sci.,5(1):41–53 (1971).

    Google Scholar 

  2. A. H. Clifford and G. B. Preston, “The algebraic theory of semigroups,”Math. Surveys 7, Vol. 1 (Amer. Math. Soc., Providence, Rhode Island, 1961).

    Google Scholar 

  3. R. McNaughton and S. Papert,Counter-Free Automata (MIT Press, 1971).

  4. M. Nivat, “Éléments de la théorie générate des codes,” in E. R. Caianiello, ed.,Automata Theory (Academic Press, New York, 1966), pp. 278–294.

    Google Scholar 

  5. M. O. Rabin and D. Scott, “Finite Automata and their decision problems,”IBM J. Res. Develop. 3(2):114–125 (1959).

    Google Scholar 

  6. M. P. Schützenberger, “On synchronizing prefix codes,”Inf. Control 11:396–401 (1967).

    Google Scholar 

  7. H. J. Shyr and G. Thierrin, “Power-separating regular languages,”Mathematical System Theory 8(1):90–95 (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Western Ontario, London, Ontario, Canada

    H. J. Shyr & G. Thierrin

Authors
  1. H. J. Shyr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Thierrin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research has been supported by Grant A7877 of the National Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shyr, H.J., Thierrin, G. Left-noncounting languages. International Journal of Computer and Information Sciences 4, 95–102 (1975). https://doi.org/10.1007/BF00976221

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00976221

Key words

Search

Navigation