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On ≤1−ttp-sparseness and nondeterministic complexity classes

  • Osamu Watanabe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

For any reduction r, a set is called “≤ r p -sparse” if it is ≤ r p -reducible to a sparse set. The difficulty of sets in nondeterministic complexity classes is investigated in terms of non-≤ 1−tt p -sparseness, i.e., not being ≤ 1−tt p -reducible to any sparse set. In particular, nondeterministic complexity classes used to specify various types of one-way functions are mainly considered, i.e., UP, N(poly), UBPP, and UP. For each such class, we prove that it contains a non-≤ 1−tt p -sparse set unless it is included in P. Since these classes are included in more general nondeterministic complexity classes such as NP, easy consequences of our observations show the nonsparseness of ≤ 1−tt p -hard sets for such classes.

Keywords

Polynomial Time Complexity Class Boolean Formula Pseudo Polynomial Time Promise Problem 
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 1988

Authors and Affiliations

  • Osamu Watanabe
    • 1
  1. 1.Dept. of MathematicsUniversity of California, Santa BarbaraSanta BarbaraUSA

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