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On bounded truth-table, conjunctive, and randomized reductions to sparse sets

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 652))

Abstract

In this paper we study the consequences of the existence of sparse hard sets for NP and other complexity classes under certain types of deterministic, randomized, and nondeterministic reductions. We show that if an NP-complete set is bounded truth-table reducible to some set that conjunctively reduces to a sparse set then P=NP. We next show that if an NP-complete set is bounded truth-table reducible to some set that randomly reduces (via a co-rp reduction) to some set that conjunctively reduces to a sparse set then RP=NP. Finally, we prove that if a coNP-complete set reduces via a nondeterministic polynomial time many-one reduction to a co-sparse set then PH=Θ p2 . On the other hand, we show that nondeterministic polynomial time many-one reductions to sparse sets are as powerful as nondeterministic Turing reductions to sparse sets.

Work done while visiting Universität Ulm. Supported in part by an Alexander von Humboldt research fellowship.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, 110016, Delhi New Delhi, India

    V. Arvind

  2. Abteilung für Theoretische Informatik, Universität Ulm, Oberer Eselsberg, D-W-7900, Ulm, Germany

    J. Köbler & M. Mundhenk

Authors
  1. V. Arvind
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  2. J. Köbler
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  3. M. Mundhenk
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Editor information

Rudrapatna Shyamasundar

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© 1992 Springer-Verlag Berlin Heidelberg

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Arvind, V., Köbler, J., Mundhenk, M. (1992). On bounded truth-table, conjunctive, and randomized reductions to sparse sets. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_101

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  • DOI: https://doi.org/10.1007/3-540-56287-7_101

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  • Print ISBN: 978-3-540-56287-0

  • Online ISBN: 978-3-540-47507-1

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