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Reductions to sets of low information content

Extended abstract
  • V. Arvind
  • Y. Han
  • L. Hemachandra
  • J. Köbler
  • A. Lozano
  • M. Mundhenk
  • M. Ogiwara
  • U. Schöning
  • R. Silvestri
  • T. Thierauf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 623)

Abstract

In this paper we study the complexity of sets that reduce to sparse sets (and tally sets), and the complexity of the simplest sparse sets to which such sets reduce. We show even with respect to very flexible reductions that NP cannot have sparse hard sets unless P = NP; an immediate consequence of our results is: If any NP-complete set conjunctively reduces to a sparse set, then P = NP. We also show that any set A that reduces to some sparse set (via various types of reductions) in fact reduces by the same type of reduction to a sparse set that is simple relative to A. We give a complete characterization of the sets of low instance complexity in terms of reductions to tally sets; it follows that if P ≠ NP, then no set of low instance complexity can be complete for NP with respect to disjunctive reductions or conjunctive reductions.

Keywords

IEEE Computer Society Complexity Theory SIAM Journal Polynomial Hierarchy Turing Reduction 
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 1992

Authors and Affiliations

  • V. Arvind
    • 1
  • Y. Han
    • 2
  • L. Hemachandra
    • 2
  • J. Köbler
    • 3
  • A. Lozano
    • 4
  • M. Mundhenk
    • 3
  • M. Ogiwara
    • 5
  • U. Schöning
    • 3
  • R. Silvestri
    • 6
  • T. Thierauf
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyDelhi, New DelhiIndia
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA
  3. 3.Abteilung für Theoretische InformatikUniversität UlmOberer EselsbergGermany
  4. 4.Department of Software (L.S.I.)Universität Politècnica de CatalunyaBarcelonaSpain
  5. 5.Department of Computer Science and Information MathematicsUniversity of Electro-CommunicationsTokyoJapan
  6. 6.Dipartimento Di MatematicaUniversitá degli Studi di Roma, “La Sapienza”RomeItaly

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