Decision versus search problems in super-polynomial time

Russell Impagliazzo, Gabor Tardos

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

23 Citations (Scopus)

Abstract

The following propositions are considered: (1) E = NE (i.e., it is decidable in exponential time whether there is a solution for an exponential-type search problem). (2) Every exponential-type search problem is solvable in exponential time. (3) The first solution to every exponential-type search problem can be found in exponential time. (4) E = ENP. It is easy to see that (4) implies (3) implies (2) implies (1). It has been conjectured that the first and last of these assumptions are equivalent in every relativized world. It is proved here that there exist relativized words in which the last two implications are not reversible. This is evidence that the search problem is not reducible to decision problems in exponential time. It is also proved that the third and fourth assumptions are equivalent. The combinatorial core of the separation results is a lower bound on the parallel complexity of a generalized version of the X-search problem.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherPubl by IEEE
Pages222-227
Number of pages6
ISBN (Print)0818619821
Publication statusPublished - Nov 1 1989
Event30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA
Duration: Oct 30 1989Nov 1 1989

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

Other

Other30th Annual Symposium on Foundations of Computer Science
CityResearch Triangle Park, NC, USA
Period10/30/8911/1/89

ASJC Scopus subject areas

  • Hardware and Architecture

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  • Cite this

    Impagliazzo, R., & Tardos, G. (1989). Decision versus search problems in super-polynomial time. In Annual Symposium on Foundations of Computer Science (Proceedings) (pp. 222-227). (Annual Symposium on Foundations of Computer Science (Proceedings)). Publ by IEEE.