Skip to main content

Testing membership: Beyond permutation groups

Extended abstract

  • Contributed Papers
  • Conference paper
  • First Online:
  • 152 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 349))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Babai, E. Luks and A. Seress, Permutation Groups in NC, Proc. of the 19th ACM Symp. on the Theory of Computing (1987), pp. 409–420.

    Google Scholar 

  2. D. Mix Barrington, N. Immerman and H. Straubing, On uniformity within NC1, Proc. of the 3rd Annual Conf. on the Structure in Complexity Theory, IEEE Computer Society Press (1988), pp. 47–59.

    Google Scholar 

  3. M. Beaudry, Testing membership in commutative transformation semigroups, Proc. of the 14th International Colloquium on Automata, Languages and Programming, Springer Lecture Notes in Comp. Sci. 267 (1987), pp. 542–549.

    Google Scholar 

  4. M. Beaudry, Membership Testing in Transformation Monoids, Doctoral Thesis, School of Computer Science, Tech. Rep. TR-SOCS-88.2, McGill University (1988).

    Google Scholar 

  5. S.R. Buss, The boolean formula value problem is in ALOGTIME, Proc. of the 19th ACM Symp. on the Theory of Computing (1987), pp. 123–131.

    Google Scholar 

  6. S.A. Cook, The complexity of theorem-proving procedures Proc. of the 3rd ACM Symp. on the Theory of Computing (1971), pp. 151–158.

    Google Scholar 

  7. S.A. Cook, A taxonomy of problems with fast parallel solutions, Information and Computation64 (1985), pp. 2–22.

    Google Scholar 

  8. S. Eilenberg, Automata, Languages and Machines, Vol. B, Academic Press (1976).

    Google Scholar 

  9. C. Fennemore, All varieties of bands, Semigroup Forum1 (1970), pp. 172–177.

    Google Scholar 

  10. C. Fennemore, All varieties of bands I, II, Mathematische Nachrichten48 (1971), pp. 237–252 and 253–262.

    Google Scholar 

  11. M. Furst, J. Hopcroft and E. Luks, Polynomial time algorithms for permutation groups, Proc. of the 21st IEEE Symp. on the Foundations of Computer Science (1980), pp. 36–41.

    Google Scholar 

  12. J.A. Gerhard, The lattice of equational classes of idempotent semigroups, J. of Algebra15 (1970), pp. 195–224.

    Google Scholar 

  13. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley (1979).

    Google Scholar 

  14. N.D. Jones and W.T. Laaser, Complete problems for deterministic polynomial time, Theoretical Computer Science3 (1977), pp. 105–117.

    Google Scholar 

  15. D. Kozen, Lower bounds for natural proof systems, Proc. of the 18th ACM Symp. on the Theory of Computing (1977), pp. 254–266.

    Google Scholar 

  16. K. Krohn and J.L. Rhodes, Algebraic theory of machines, I. Prime decomposition theorem for finite semigroups and machines, Trans. Amer. Math. Soc.116 (1965), pp. 450–464.

    Google Scholar 

  17. G. Lallement, Semigroups and Combinatorial Applications, Addison-Wesley (1979).

    Google Scholar 

  18. E.M. Luks and P. McKenzie, Fast parallel computation with permutation groups, Proc. of the 26th IEEE Symp. on the Foundations of Computer Science (1985), pp. 505–514.

    Google Scholar 

  19. E.M. Luks, Parallel algorithms for permutation groups and graph isomorphism, Proc. of the 27th IEEE Symp. on the Foundations of Computer Science (1986), pp. 292–302.

    Google Scholar 

  20. P. McKenzie and S.A. Cook, The parallel complexity of the Abelian permutation group membership problem, Proc. of the 24th IEEE Symp. on the Foundations of Computer Science (1983), pp. 154–161.

    Google Scholar 

  21. P. McKenzie and S.A. Cook, The parallel complexity of Abelian permutation groups problems, SIAM J. on ComputingVol. 16, no. 5 (Oct. 1987), pp. 880–909.

    Google Scholar 

  22. J.-E. Pin, Variétés de langages formels, Masson (1984).

    Google Scholar 

  23. N. Pippenger, On simultaneous resource bounds, Proc. of the 20th IEEE Symp. on the Foundations of Computer Science (1979), pp. 307–311.

    Google Scholar 

  24. C.C. Sims, Computational methods in the study of permutation groups, in Computational Problems in Abstract Algebra, ed. J. Leech, Pergamon Press (1970), pp. 169–183.

    Google Scholar 

  25. J. Stern, Complexity of some problems from the theory of automata, Information and Computation66 (1985), pp. 163–176.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

B. Monien R. Cori

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beaudry, M., McKenzie, P., Thérien, D. (1989). Testing membership: Beyond permutation groups. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029001

Download citation

  • DOI: https://doi.org/10.1007/BFb0029001

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50840-3

  • Online ISBN: 978-3-540-46098-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics