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)


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.


Dominance Condition Distributional Problem Partial Assignment Standard Distribution Equivalent Formula 
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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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