P-selective sets and reducing search to decision vs self-reducibility

Edith Hemaspaandra, Ashish V. Naik, Mitsunori Ogihara, Alan L. Selman

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

We distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. Results include: (i) If NE ≠ E, then there exists a set t in NP - P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L and L is not self-reducible, (ii) If UE ≠ E, then there exists a language L ∈ UP - P such that search nonadaptively reduces to decision for L, but L is not self-reducible, (iii) If UE ∩ co-UE ≠ E, then there is a disjunctive self-reducible language L ∈ UP - P for which search does not nonadaptively reduce to decision. We prove that if NE ⊈ BPE, then there is a language L ∈ NP - BPP such that L is randomly self-reducible, not nonadaptively randomly self-reducible, and not self-reducible. We obtain results concerning trade-offs in multiprover interactive proof systems and results that distinguish checkable languages from those that are nonadaptively checkable. Many of our results are proven by constructing p-selective sets. We obtain a p-selective set that is not ≤ Ptt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ PT-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ Pm-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.

Original languageEnglish (US)
Pages (from-to)194-209
Number of pages16
JournalJournal of Computer and System Sciences
Volume53
Issue number2
DOIs
StatePublished - Oct 1996
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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