Relationships among PL, #L, and the determinant

Eric Allender, Mitsunori Ogihara

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

13 Scopus citations

Abstract

Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Annual Structure in Complexity Theory Conference
Editors Anon
PublisherPubl by IEEE
Pages267-278
Number of pages12
ISBN (Print)0818656727
StatePublished - Dec 1 1994
Externally publishedYes
EventProceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth
Duration: Jun 28 1994Jul 1 1994

Publication series

NameProceedings of the IEEE Annual Structure in Complexity Theory Conference
ISSN (Print)1063-6870

Other

OtherProceedings of the 9th Annual Structure in Complexity Theory Conference
CityAmsterdam, Neth
Period6/28/947/1/94

ASJC Scopus subject areas

  • Engineering(all)

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