On Span Programs

M. Karchmer*, A. Wigderson

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

409 Scopus citations

Abstract

We introduce a linear algebraic model of computation, the Span Program, and prove several upper and lower bounds on it. These results yield the following applications in complexity and cryptography: SL is contained in ⊕L (a weak Logspace analogue of NP is contained in ⊕P), the first superlinear size lower bounds on branching programs that count, and a broader class of functions which possess information-theoretic secret sharing schemes. The proof of the main connection, between Span Programs and counting branching programs, uses a variant of Razborov's general approximation method.

Original languageEnglish
Title of host publicationProceedings of the Eighth Annual Structure in Complexity Theory Conference
Editors Anon
PublisherPubl by IEEE
Pages102-111
Number of pages10
ISBN (Print)0818640715
StatePublished - 1993
Externally publishedYes
EventProceedings of the Eighth Annual Structure in Complexity Theory Conference - San Diego, California
Duration: 18 May 199321 May 1993

Publication series

NameProceedings of the Eighth Annual Structure in Complexity Theory Conference

Conference

ConferenceProceedings of the Eighth Annual Structure in Complexity Theory Conference
CitySan Diego, California
Period18/05/9321/05/93

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