Advertisement

Characterizations of some complexity classes between Θ2p and Δ2p

  • Jorge Castro
  • Carlos Seara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We give some characterizations of the classes P NP [O(log k n)]. First, we show that these classes are equal to classes ACk−1(NP). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. As a last characterization, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an NP oracle and classes defined by small size circuits with NP oracle gates. With these results we solve open questions that arose in [Wa-90] and [AW-90]. Finally, we give an oracle relative to which classes P NP [O(log k n)] and P NP [O(logk+1n)] are different.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AW-90]
    E. Allender, C. B. Wilson, Width-Bounded Reducibility and Binary Search over Complexity Classes, Proc. 5th IEEE Conf. on Structure in Complexity Theory, (1990), pp. 122–129.Google Scholar
  2. [Be-87]
    R. J. Beigel, Bounded queries to SAT and the Boolean hierarchy, To appear in TCS.Google Scholar
  3. [BH-91]
    S. Buss, L. Hay, On truth-table reducibility to SAT, Information and Computation, vol. 91 (1991), pp. 86–102.Google Scholar
  4. [CH-86]
    J. Cai, L. A. Hemachandra, The Boolean hierarchy: hardware over NP, Proc. 1st IEEE Conf. on Structure in Complexity Theory, (1986), pp. 105–124.Google Scholar
  5. [Co-85]
    S. Cook, A taxonomy of problems with fast parallel algorithms, Information and Control, vol. 64 (1985), pp. 2–22.Google Scholar
  6. [KSW-87]
    J. Köbler, U. Schöning, K. W. Wagner, The difference and the truth-table hierarchies for NP, R.A.I.R.O. 21 (1987), pp. 419–435.Google Scholar
  7. [LT-91]
    A. Lozano, J. Torán, Self-reducible sets of small density, Math. Systems Theory 24 (1991), pp. 83–100Google Scholar
  8. [Wa-90]
    K. W. Wagner, Bounded query classes, SIAM J. Comput., vol. 19, 5 (1990), pp. 833–846.Google Scholar
  9. [WW-85]
    G. Wechsung, K. W. Wagner, On the Boolean closure of NP, manuscript 1985 (extended abstract as: Wechsung G., On the Boolean closure of NP, Proc. Conf. Wundam. Comp. Theory, Cottbus 1985, LNCS 199 (1985), pp. 485–493).Google Scholar
  10. [Wi-87]
    C. B. Wilson, Relativized NC, Math. Systems Theory, vol. 20 (1987), pp. 13–29.Google Scholar
  11. [Wi-90]
    C. B. Wilson, Decomposing NC and AC, SIAM J. Comput., vol. 19, 2 (1990), pp. 384–396.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jorge Castro
    • 1
  • Carlos Seara
    • 2
  1. 1.Dept. Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Dept. Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations