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Counting, selecting, and sorting by query-bounded machines

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STACS 93 (STACS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

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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 (x 1, x 2,..., 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 (x 1, x 2,..., x k ) if such a string exists and to sort the input (x 1, x 2,..., x k ) with respect to the ordering x ≼ y if and only if x ∈ A ⇒ y ∈ 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.

Research supported by a Deutsche Forschungsgesellschaft Postdoktorandenstipendium.

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Authors and Affiliations

  1. Fachbereich Informatik, Technische Universität Berlin, FR 6-2 Franklinstr. 28-29, 1000, Berlin 10, Germany

    Albrecht Hoene & Arfst Nickelsen

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  1. Albrecht Hoene
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  2. Arfst Nickelsen
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P. Enjalbert A. Finkel K. W. Wagner

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© 1993 Springer-Verlag Berlin Heidelberg

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Hoene, A., Nickelsen, A. (1993). Counting, selecting, and sorting by query-bounded machines. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_22

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  • DOI: https://doi.org/10.1007/3-540-56503-5_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

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