On sparse hard sets for counting classes

Mitsunori Ogihara, Antoni Lozano

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this paper, we study one-word-decreasing self-reducible sets which are introduced by Lozano and Torán (1991). These are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query and this is lexicographically smaller than the input. We show first that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact, we can prove that for any class K chosen from {PP, NP, C = P, MOD2P, MOD3 P,...} it holds that (1) if there is a sparse ≤P btt-hard set for K then K ⊆ P, and (2) if there is a sparse ≤SN btt-hard set for K then K ⊆ NP {frown} co-NP. This generalizes the result of Ogiwara and Watanabe (1991) to the mentioned complexity classes.

Original languageEnglish (US)
Pages (from-to)255-275
Number of pages21
JournalTheoretical Computer Science
Volume112
Issue number2
DOIs
StatePublished - May 10 1993
Externally publishedYes

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Counting
Complexity Classes
Reducibility
Predicate
Class
Query
Path
Generalise

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

On sparse hard sets for counting classes. / Ogihara, Mitsunori; Lozano, Antoni.

In: Theoretical Computer Science, Vol. 112, No. 2, 10.05.1993, p. 255-275.

Research output: Contribution to journalArticle

Ogihara, Mitsunori ; Lozano, Antoni. / On sparse hard sets for counting classes. In: Theoretical Computer Science. 1993 ; Vol. 112, No. 2. pp. 255-275.
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