Skip to main content
SpringerLink
Log in

Testing for a Semilattice Term

  • Published:
Order Aims and scope Submit manuscript

Abstract

This paper investigates the computational complexity of deciding if a given finite algebra is an expansion of a semilattice. In general this problem is known to be EXP-TIME complete, and we show that even for idempotent algebras, this problem remains hard. This result is in contrast to a series of results that show that similar decision problems turn out to be tractable.

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. Baker, K.A.: Congruence-distributive polynomial reducts of lattices. Algebra Univers. 9(1), 142–145 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barto, L., Krokhin, A., Willard, R.: Polymorphisms, and how to use them. In: Krokhin, A., Zivny, S. (eds.) The Constraint Satisfaction Problem: Complexity and Approximability, volume 7 of Dagstuhl Follow-Ups, pp. 1–44. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl (2017)

  3. Bergman, C.: Universal Algebra, Volume 301 of Pure and Applied Mathematics (Boca Raton). CRC Press, Boca Raton (2012). Fundamentals and selected topics

    Google Scholar 

  4. Bergman, C., Juedes, D., Slutzki, G.: Computational complexity of term-equivalence. Int. J. Algebra Comput. 9(1), 113–128 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra, Volume 78 of Graduate Texts in Mathematics. Springer, New York-Berlin (1981)

    MATH  Google Scholar 

  6. Freese, R., Valeriote, M.A.: On the complexity of some Maltsev conditions. Int. J. Algebra Comput. 19(1), 41–77 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Freese, R., Kiss, E., Valeriote, M.: Universal Algebra Calculator. Available at: www.uacalc.org (2011)

  8. Hobby, D., McKenzie, R.: The Structure of Finite Algebras, Volume 76 of Contemporary Mathematics. American Mathematical Society, Providence (1988). Revised edition: 1996

    Book  MATH  Google Scholar 

  9. Horowitz, J.: Computational complexity of various Mal’cev conditions. Int. J. Algebra Comput. 23(6), 1521–1531 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jónsson, B.: Algebras whose congruence lattices are distributive. Math. Scand. 21(1968), 110–121 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kazda, A., Valeriote, M.: Deciding some Maltsev conditions in finnite idempotent algebras. Preprint (2017)

  12. Kearnes, K.A., Kiss, E.W.: The shape of congruence lattices. Mem. Am. Math. Soc. 222(1046), viii+ 169 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Taylor, W.: Simple equations on real intervals. Algebra Univers. 61(2), 213–226 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Valeriote, M., Willard, R.: Idempotent n-permutable varieties. Bull. Lond. Math. Soc. 46(4), 870–880 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The first author was supported by the National Science Foundation under grant No. 1500235 and the third author was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

Author information

Authors and Affiliations

  1. University of Hawaii at Manoa, Honolulu, HI, USA

    Ralph Freese & J. B. Nation

  2. McMaster University, Hamilton, ON, Canada

    Matt Valeriote

Authors
  1. Ralph Freese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. B. Nation
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matt Valeriote
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matt Valeriote.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Freese, R., Nation, J.B. & Valeriote, M. Testing for a Semilattice Term. Order 36, 65–76 (2019). https://doi.org/10.1007/s11083-018-9455-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-018-9455-6

Keywords

Search

Navigation