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Counting, selecting, and sorting by query-bounded machines

  • Albrecht Hoene
  • Arfst Nickelsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

We study the query-complexity of counting, selecting, and sorting functions. That is, for a given set A and a positive integer k, we ask, how many queries to an arbitrary oracle does a polynomial-time machine on input (x1, x2,..., x k ) need to determine how many strings of the input are in A. We also ask how many queries are necessary to select a string in A from the input (x1, x2,..., x k ) if such a string exists and to sort the input (x1, x2,..., x k ) with respect to the ordering xy if and only if x ∈ Ay ∈ A. We obtain optimal query-bounds for these problems, and show that sets for which these functions have a low query-complexity must be easy in some sense. For such sets we obtain optimal placements in the extended low hierarchy. We also show that in the case of NP-complete sets the lower bounds for counting and selecting hold unless P=NP. Finally, we relate these notions to cheatability and p-superterseness. Our results yield as corollaries extensions of previously know results.

Keywords

Selector Function Query Tree Pruning Step Sorting Function SlAM Journal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Albrecht Hoene
    • 1
  • Arfst Nickelsen
    • 1
  1. 1.Fachbereich InformatikTechnische Universität BerlinBerlin 10Germany

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