Generalized theorems on relationships among reducibility notions to certain complexity classes

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6 Scopus citations


In this paper we give several generalized theorems concerning reducibility notions to certain complexity classes. We study classes that are either (I) closed under NP many-one reductions and polynomial-time conjunctive reductions or (II) closed under coNP many-one reductions and polynomial-time disjunctive reductions. We prove that, for such a class K, (1) reducibility notions of sets to K under polynomial-time constant-round truth-table reducibility, polynomial-time log-Turing reducibility, logspace constant-round truth-table reducibility, logspace log-Turing reducibility, and logspace Turing reducibility are all equivalent and (2) every set that is polynomial-time positive Turing reducible to a set in K is already in K. From these results, we derive some observations on the reducibility notions to C=P and NP.

Original languageEnglish (US)
Pages (from-to)189-200
Number of pages12
JournalMathematical systems theory
Issue number3
StatePublished - May 1 1994
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics


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