Skip to main content
SpringerLink
Log in

Checking quasi-identities in a finite semigroup may be computationally hard

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We exhibit a 10-element semigroup Q such that the question “Does a given quasi-identity hold in Q?” is co-NP-complete while the question “Does a given identity hold in Q?” can be answered in linear time.

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. Bergman, C., and G. Slutzki, ‘Complexity of some problems concerning varieties and quasi-varieties of algebras’, SIAM J. Comput. 30:359–382, 2000.

    Google Scholar 

  2. Clifford, A. H., and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Amer. Math. Soc., 1961.

  3. Garey, M. R., and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, 1979.

  4. Klíma, O., ‘Complexity issues of checking identities in finite monoids’, submitted.

  5. Mashevitsky, G. I., ‘On identities in varieties of completely simple semigroups over abelian groups’, Modern Algebra, Leningrad, 81–89, 1978 (in Russian).

  6. Ore, O., Theory of Graphs, Amer. Math. Soc., 1962.

  7. Papadimitriou, C. H., Computational Complexity, Addison-Wesley Publishing Company, 1994.

  8. Seif, S., ‘The Perkins semigroup has co-NP-complete term-equivalence problem’, submitted.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, Ural State University, Lenina 51, Ekaterinburg, Russua

    M. V. Volkov

Authors
  1. M. V. Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volkov, M.V. Checking quasi-identities in a finite semigroup may be computationally hard. Stud Logica 78, 349–356 (2004). https://doi.org/10.1007/s11225-005-0356-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-0356-5

Keywords

Search

Navigation