On polynomial-time bounded truth-table reducibility of NP sets to sparse sets

Mitsunori Ogiwara, Osamu Watanabe

Research output: Contribution to journalArticle

83 Scopus citations

Abstract

It is proved that if P ≠ NP, then there exists a set in NP that is not polynomial-time bounded truth-table reducible (in short, ≤bttP-reducible) to any sparse set. In other words, it is proved that no sparse ≤bttP-hard set exists for NP unless P = NP. By using the technique proving this result, the intractability of several number-theoretic decision problems, i.e., decision problems defined naturally from number-theoretic problems is investigated. It is shown that for these number-theoretic decision problems, if it is not in P, then it is not ≤bttP-reducible to any sparse set.

Original languageEnglish (US)
Pages (from-to)471-483
Number of pages13
JournalSIAM Journal on Computing
Volume20
Issue number3
DOIs
StatePublished - Jan 1 1991
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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