Skip to main content

Containment, separation, complete sets, and immunity of complexity classes

  • Conference paper
  • First Online:
Book cover Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

Included in the following conference series:

Supported in part by an NSF grant DCR-8301766. Part of the second author's work was performed at Cornell University.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

7. References

  1. L. Berman, On the structure of complete sets: Almost everywhere complexity and infinitely often speedup, Proc. 17th IEEE FOCS (1977), 76–80.

    Google Scholar 

  2. L. Berman, Polynomial reducibility and complete sets, Ph.D. thesis, Cornell University, May 1977.

    Google Scholar 

  3. R. Book, Tally languages and complexity classes, Information and Control 26 (1974), pp. 186–193.

    Google Scholar 

  4. R. Book, S. Greibach, and B. Wegbreit, Time-and tape-bound Turing acceptors and AFL's, JCSS 4,6 (Dec. 1970) pp. 606–621.

    Google Scholar 

  5. R. Rook and U. Schoning, Immunity, relativization and nondeterminism, to appear in SIAM J. Computing.

    Google Scholar 

  6. S. Cook, A hierarchy for nondeterministic time complexity, JCSS 7,4 (1973) pp. 343–353.

    Google Scholar 

  7. S. Homer, On simple and creative sets in NP. TR# 84/002, Department of Computer Science, Boston University.

    Google Scholar 

  8. J. Hartmanis, On sparse sets in NP-P, Inf. Proc. Let. 2 (1983) pp. 55–60.

    Google Scholar 

  9. J. Hartmanis and N. Immerman, On complete sets in NPCoNP, 12th ICALP, Napflion, Greece. 1985.

    Google Scholar 

  10. J. Hartmanis, N. Immerman, and V. Sewelson, On sparse sets in NP-P. EXPTIME vs. NEXPTIME, Proc. 15th ACM STOC (April 1983), pp. 382–391.

    Google Scholar 

  11. J. Hartmanis, P. Lewis, and R. Stearns, Classification of computations by time and memory requirements, Proc. IFIP Congress 65, Spartan, NY. (1965). pp. 31–35.

    Google Scholar 

  12. J. Hartmanis and Y. Yesha, Computation times of NP sets of different densities, 10th ICALP, Spain (1983). Also, Special Issue of Theor. Comp. Sci. 34 (1984) pp. 17–32.

    Google Scholar 

  13. J. Hopcroft and J. Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley (1979).

    Google Scholar 

  14. W. Kowalozyk, Some connections between presentability of complexity classes and the power of formal systems of reasoning, Proc. MFCS'84 pp. 364–369.

    Google Scholar 

  15. N. Lynch, On reducibility to complex or sparse sets, J. ACM, 22, (1975) pp. 341–345.

    Google Scholar 

  16. N. Lynch, M. Fischer, and A. Meyer, Relativization of the theory of computational complexity, Trans. AMS.

    Google Scholar 

  17. M. Li, Lower bounds in computational complexity, Ph.D. Thesis, Cornell University (1985).

    Google Scholar 

  18. L. Landweber, R. Lipton, and E. Robertson, On the structure of sets in NP and other complexity classes, Theor. Comp. Sci., 18(1982) pp. 95–103.

    Google Scholar 

  19. R. Ladner, N. Lynch, and A. Selman, Comparison of polynomial time reducibilities, Proc. STOC (1974) pp. 110–121.

    Google Scholar 

  20. S. Mahaney, Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis, Proc. IEEE FOCS, 1980, pp. 54–60.

    Google Scholar 

  21. P. Orponen and U. Schoning, On the density of polynomial complexity cores, Proc. Math. Found. Comp. Sci. — 84, Lecture Notes in Computer Science, to appear.

    Google Scholar 

  22. C. W. Rackoff and J. I. Seiferas, Limitations on separating nondeterministic complexity classes, 10, 4 SIAM Comp. (1981), pp. 742–745.

    Google Scholar 

  23. J. Seiferas, M. Fischer, and A. Meyer, Separating nondeterministic time classes, JACM, 25, 1, (1978) pp. 146–167.

    Google Scholar 

  24. M. Sipser, On relativization and the existence of complete sets, 9th ICALP, Lecture Notes in Computer Science, Springer Verlag, Berlin (1982) pp. 523–531.

    Google Scholar 

  25. Y. Yesha, On certain polynomial-time truth-table reducibilities of complete sets to sparse sets, SIAM J. Comp. 12,3 (1983).

    Google Scholar 

  26. S. Zak, A Turing machine hierarchy, to appear in Theor. Comp. Sci.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Laurent Kott

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hartmanis, J., Li, M., Yesha, Y. (1986). Containment, separation, complete sets, and immunity of complexity classes. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_63

Download citation

  • DOI: https://doi.org/10.1007/3-540-16761-7_63

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics