Bounded Query Classes

  title={Bounded Query Classes},
  author={Klaus W. Wagner},
  journal={SIAM J. Comput.},
  • K. Wagner
  • Published 1990
  • Mathematics, Computer Science
  • SIAM J. Comput.
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 or the way in which the queries are made is restricted (e.g., queries made during truth-table reductions). Very different kinds of such restrictions result in the same or comparable complexity classes. In particular, the class $P^{\text{NP}}[O(\log n)]$ can be characterized in very different ways. Furthermore, the Boolean hierarchy is… Expand
Restricted information from nonadaptive queries to NP
  • Yenjo Han, T. Thierauf
  • Mathematics, Computer Science
  • Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference
  • 1995
We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators do not have full access to the answers to the queries but get only restrictedExpand
Restricted Information from Nonadaptive Queries to NP
We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators donothave full access to the answers to the queries but get only restrictedExpand
Adaptive versus nonadaptive queries to NP and p-selective sets
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If certain logics are of the same expressibility then the Polynomial Hierarchy collapses and some new complete problems for the complexity class LNP via projection translations are exhibited. Expand
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It is shown that the strongest type of the semantically restricted polynomial time oracle machines w.r.t. NP oracles is the weakest w.R.T. sparse oracles. Expand
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Bounded Queries to SAT and the Boolean Hierarchy
  • R. Beigel
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1991
The complexity of decision problems that can be solved by a polynomial-time Turing machine that makes a bounded number of queries to an NP oracle is studied and the Boolean hierarchy and the bounded query hierarchies either stand or collapse together are studied. Expand
Some Connections between Bounded Query Classes and Non-Uniform Complexity (Long Version)
Abstract Let A(x) be the characteristic function of A. Consider the function Fk (x1, . . . , xk) = A(x1) · · ·A(xk). We show that if Fk can be computed with fewer than k queries to some set X then AExpand
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The structure of the boolean hierarchy and its relations with more common classes is emphasized: separation and immunity results, complete languages, upward separations, connections to sparse oracles for NP, and structural asymmetries between complementary classes. Expand
The Polynomial Time Hierarchy Collapses if the Boolean Hierarchy Collapses
  • Jim Kadin
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1988
It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that ${\text{co-NP}} \subseteq {\text{ NP}}^S $, and therefore the polynomial time hierarchy (PH) col...