On the reducibility of sets inside NP to sets with low information content

Mitsunori Ogihara, Till Tantau

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper studies for various natural problems in NP whether they can be reduced to sets with low information content, such as branches, P-selective sets, and membership comparable sets. The problems that are studied include the satisfiability problem, the graph automorphism problem, the undirected graph accessibility problem, the determinant function, and all logspace self-reducible languages. Some of these are complete for complexity classes within NP, but for others an exact complexity theoretic characterization is not known. Reducibility of these problems is studied in a general framework introduced in this paper: prover-verifier protocols with low-complexity provers. It is shown that all these natural problems indeed have such protocols. This fact is used to show, for certain reduction types, that these problems are not reducible to sets with low information content unless their complexity is much less than what it is currently believed to be. The general framework is also used to obtain a new characterization of the complexity class L:L is the class of all logspace self-reducible sets in LL-sel.

Original languageEnglish (US)
Pages (from-to)499-524
Number of pages26
JournalJournal of Computer and System Sciences
Volume69
Issue number4
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

Keywords

  • Computational complexity
  • Membership comparability
  • Prover-verifier protocols
  • Selectivity
  • Self-reduction
  • Sets with low information content

ASJC Scopus subject areas

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

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