Lower bounds for monotone span programs

Amos Beimel; Mike Paterson; Anna Gál

doi:10.1007/BF01202040

Lower bounds for monotone span programs

Amos Beimel
, Mike Paterson
, Anna Gál

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

Span programs provide a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for formula size, symmetric branching programs, and contact schemes. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. We prove a lower bound of Ω(m^2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.

Original language	English
Pages (from-to)	29-45
Number of pages	17
Journal	Computational Complexity
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/BF01202040
State	Published - 1 Jan 1996
Externally published	Yes

Keywords

Lower bounds
Monotone complexity classes
Secret sharing
Span programs

ASJC Scopus subject areas

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics
Computational Mathematics

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10.1007/BF01202040

Cite this

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title = "Lower bounds for monotone span programs",

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AB - Span programs provide a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for formula size, symmetric branching programs, and contact schemes. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. We prove a lower bound of Ω(m2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.

KW - Lower bounds

KW - Monotone complexity classes

KW - Secret sharing

KW - Span programs

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Lower bounds for monotone span programs

Abstract

Keywords

ASJC Scopus subject areas

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