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Comparing Reductions to NP-Complete Sets

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Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4051))

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Abstract

Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following:

  1. 1

    Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete.

  2. 2

    Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-complete for NP but not Turing-complete.

  3. 3

    Every problem that is many-one complete for NP is complete under length-increasing reductions that are computed by polynomial-size circuits.

The first item solves one of Lutz and Mayordomo’s “Twelve Problems in Resource-Bounded Measure” (1999). We also show that every problem that is complete for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Wyoming,  

    John M. Hitchcock

  2. Department of Computer Science, Iowa State University,  

    A. Pavan

Authors
  1. John M. Hitchcock
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  2. A. Pavan
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Hitchcock, J.M., Pavan, A. (2006). Comparing Reductions to NP-Complete Sets. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_41

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  • DOI: https://doi.org/10.1007/11786986_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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