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On the Difference between Polynomial-Time Many-One and Truth-Table Reducibilities on Distributional Problems

  • Shin Aida
  • Rainer Schuler
  • Tatsuie Tsukiji
  • Osamu Watanabe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

In this paper we separate many-one reducibility from truth- table reducibility for distributional problems in Dist NP under the hy- pothesis that PNP . As a first example we consider the 3-Satisfiability problem (3SAT) with two different distributions on 3CNF formulas. We show that 3SAT using a version of the standard distribution is truth-table reducible but not many-one reducible to 3SAT using a less redundant distribution unless P = NP.

We extend this separation result and define a distributional complexity class C with the following properties: (1) C is a subclass of Dist NP , this relation is proper unless P = NP. (2) C contains Dist P , but it is not contained in Ave P unless Dist NP ≠ Ave ZPP. (3) C has a ≤p m-complete set. (4) C has a ≤p tt-complete set that is not ≤p m-complete unless P = NP. This shows that under the assumption that PNP , the two complete- ness notions differ on some non-trivial subclass of Dist NP.

Keywords

Dominance Condition Distributional Problem Partial Assignment Standard Distribution Equivalent Formula 
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 2001

Authors and Affiliations

  • Shin Aida
    • 1
  • Rainer Schuler
    • 2
  • Tatsuie Tsukiji
    • 1
  • Osamu Watanabe
    • 2
  1. 1.School of Informatics and SciencesNagoya UniversityNagoya
  2. 2.Dept. of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyo

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