@inproceedings{a742e3262a854235a09b8fc3f28f2e7e,

title = "Counting classes are at least as hard as the polynomial-time hierarchy",

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.",

author = "Seinosuke Toda and Mitsunori Ogiwara",

year = "1991",

month = dec,

day = "1",

language = "English (US)",

isbn = "0818622555",

series = "Proc 6 Annu Struct Complexity Theor",

publisher = "Publ by IEEE",

pages = "2--12",

booktitle = "Proc 6 Annu Struct Complexity Theor",

note = "Proceedings of the 6th Annual Structure in Complexity Theory Conference ; Conference date: 30-06-1991 Through 03-07-1991",

}