Skip to main content

On restricting the access to an NP-oracle

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 317))

Included in the following conference series:

Abstract

Polynomial time machines having restricted access to an NP oracle are investigated. Restricted access means that the number of queries to the oracle is restricted and/or the way in which the queries are made is restricted. Very different kinds of such restrictions result in the same or comparable complexity classes. In particular, the class PNP[O(log n)] can be characterized in very different ways.

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.

9. References

  1. Beigel, R.J., Bounded Queries to SAT and the Boolean hierarchy, manuscript 1987.

    Google Scholar 

  2. Book, R.V., Long, T.J., Selman, A.L., Quantitative relativization of complexity classes, SIAM J. Comput. 13(1984), 461–487.

    Google Scholar 

  3. Buss, S.R., Hay, L., On truth-table reducibility to SAT and the difference hierarchy over NP, to appear in Proc of 3rd Conf. on Structure in Complexity Theory (1988).

    Google Scholar 

  4. Cai, J., Hemachandra, L.A., The Boolean hierarchy: hardware over NP, Proc. 1st Conf. on Structure in Complexity Theory (1986), LNCS 223(1986), 105–124.

    Google Scholar 

  5. [CGH2SW2 88] Cai, J., Gundermann, T., Hartmanis, J., Hemachandra, L., Sewelson, V., Wagner, K.W., Wechsung, G., The Boolean hierarchy I: Structural properties, to appear 1988 in SIAM Journal on Computing.

    Google Scholar 

  6. Gasarch, W., The complexity of optimization functions, TR 1652 (1986), Dept. of Computer Science, University of Maryland.

    Google Scholar 

  7. Hemachandra, L.A., The strong exponential hierarchy collapses, Proc. 19th. STOC Conference (1987), 110–122; see also Proc. of 2nd Conference on Structure in Complexity Theory (1987), 91.

    Google Scholar 

  8. Kadin, J., PNP[log n] and sparse Turing-complete sets for NP, Proc. of 2nd Conference on Structure in Complexity Theory (1987), 33–40.

    Google Scholar 

  9. Karp, R.M., Reducibilities among combinatorial problems, in: Complexity of Computer Computations, Plenum Press New York 1972, 85–103.

    Google Scholar 

  10. Köbler, J., Untersuchung verschiedener polynomieller Reduktionsklassen von NP, diploma thesis, University of Stuttgart 1985.

    Google Scholar 

  11. Köbler, J., personal communication.

    Google Scholar 

  12. Köbler, J., Schöning, U., Wagner, K.W., The difference and the truth-table hierarchies for NP, TR 7/86 EWH Koblenz 1986, R.A.I.R.O. 21(1987), 419–435.

    Google Scholar 

  13. Krentel, M.W., The complexity of optimization problems, Proc. 18th. Ann. STOC (1986), 69–76.

    Google Scholar 

  14. Ladner, R.E., Lynch, N.A., Relativizations of questions about log space computability, Math.Syst.Theory 10(1976), 19–32.

    Google Scholar 

  15. Ladner, R.E., Lynch, N.A., Selman, A.L., A comparison of polynomial time reducibilities, Theor. Comp. Sci. 1(1975), 103–123.

    Google Scholar 

  16. Long, T.J., On restricting the size of oracles compared with restricting access to oaracles, SIAM. J. Comput. 14(1985), 585–597.

    Google Scholar 

  17. Mahaney, S., Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis, Journ. of Comp. and Syst. Sci. 25(1982), 130–143.

    Google Scholar 

  18. Meyer, A.R., Stockmeyer, L.J., The equivalence problem for regular expressions with squaring requires exponential space. Proc. of 13th Ann. IEEE Symp. on Switching and Automata Theory 1972, 125–129.

    Google Scholar 

  19. Papadimitriou, C.H., Zachos, S.K., Two remarks on the power of counting, Proc. 6th. GI Conference on Theoretical Computer Science, LNCS 145 (1983), 269–276.

    Google Scholar 

  20. Stockmeyer, L.J., The polynomial time hierarchy, TCS 3(1977), 1–22.

    Google Scholar 

  21. Wagner, K.W., More complicated questions about maxima and minima, and some closures of NP, Proc. of 13th ICALP, LNCS 226 (1986), 434–443, see also: TCS 51 (1987), 53–80.

    Google Scholar 

  22. Wagner, K.W., Number-of-query hierarchies, Report No. 158 (1987) Institute of Mathematics, University of Augsburg.

    Google Scholar 

  23. Wagner, K.W., Bounded query computations, Proc. of 3rd Conf. on Structure in Complexity Theory (1988)

    Google Scholar 

  24. Wechsung, G., Wagner, K.W., On the Boolean closure of NP, manuscript 1985 (extended abstract as: Wechsung, G., On the Boolean closure of NP, Proc. Conf. Fundam. Comp. Theory, Cottbus 1985, LNCS 199(1985), 485–493.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Timo Lepistö Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wagner, K.W. (1988). On restricting the access to an NP-oracle. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_150

Download citation

  • DOI: https://doi.org/10.1007/3-540-19488-6_150

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19488-0

  • Online ISBN: 978-3-540-39291-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics