Lower bounds for monotone span programs

Amos Beimel; Anna Gal; Mike Paterson

doi:10.1109/sfcs.1995.492669

Lower bounds for monotone span programs

Amos Beimel, Anna Gal, Mike Paterson

Research output: Contribution to journal › Conference article › peer-review

11 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 for 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, and 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)	674-681
Number of pages	8
Journal	Annual Symposium on Foundations of Computer Science - Proceedings
DOIs	https://doi.org/10.1109/sfcs.1995.492669
State	Published - 1 Jan 1995
Externally published	Yes
Event	Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science - Milwaukee, WI, USA Duration: 23 Oct 1995 → 25 Oct 1995

ASJC Scopus subject areas

Hardware and Architecture

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10.1109/sfcs.1995.492669

Cite this

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title = "Lower bounds for monotone span programs",

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 for 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, and prove a lower bound of Ω(m2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.",

author = "Amos Beimel and Anna Gal and Mike Paterson",

year = "1995",

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doi = "10.1109/sfcs.1995.492669",

language = "English",

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journal = "Annual Symposium on Foundations of Computer Science - Proceedings",

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note = "Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science ; Conference date: 23-10-1995 Through 25-10-1995",

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AU - Beimel, Amos

AU - Gal, Anna

AU - Paterson, Mike

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N2 - Span programs provide a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for formula size, symmetric branching programs and for 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, and prove a lower bound of Ω(m2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.

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 for 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, and prove a lower bound of Ω(m2.5) for the 6-clique function. Our results improve on the previously known bounds for explicit functions.

UR - http://www.scopus.com/inward/record.url?scp=0029513522&partnerID=8YFLogxK

U2 - 10.1109/sfcs.1995.492669

DO - 10.1109/sfcs.1995.492669

M3 - Conference article

AN - SCOPUS:0029513522

SN - 0272-5428

SP - 674

EP - 681

JO - Annual Symposium on Foundations of Computer Science - Proceedings

JF - Annual Symposium on Foundations of Computer Science - Proceedings

T2 - Proceedings of the 1995 IEEE 36th Annual Symposium on Foundations of Computer Science

Y2 - 23 October 1995 through 25 October 1995

ER -

Lower bounds for monotone span programs

Abstract

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