Counting classes are at least as hard as the polynomial-time hierarchy

Seinosuke Toda, Mitsunori Ogiwara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

It is shown that many natural counting classes are at least as computationally hard as PH (the polynomial-time hierarchy) in the following sense: for each K of the counting classes, every set in K(PH) is polynomial-time randomized many-one reducible to a set in K with two-sided exponentially small error probability. As a consequence, these counting classes are computationally harder than PH unless PH collapses to a finite level. Some other consequences are also shown.

Original languageEnglish (US)
Title of host publicationProc 6 Annu Struct Complexity Theor
PublisherPubl by IEEE
Pages2-12
Number of pages11
ISBN (Print)0818622555
StatePublished - Dec 1 1991
Externally publishedYes
EventProceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA
Duration: Jun 30 1991Jul 3 1991

Publication series

NameProc 6 Annu Struct Complexity Theor

Other

OtherProceedings of the 6th Annual Structure in Complexity Theory Conference
CityChicago, IL, USA
Period6/30/917/3/91

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Toda, S., & Ogiwara, M. (1991). Counting classes are at least as hard as the polynomial-time hierarchy. In Proc 6 Annu Struct Complexity Theor (pp. 2-12). (Proc 6 Annu Struct Complexity Theor). Publ by IEEE.