On the degree of boolean functions as real polynomials

Noam Nisan, Mario Szegedy

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

52 Scopus citations

Abstract

Every boolean function may be represented as a real polynomial. In this paper we characterize the degree of this polynomial in terms of certain combinatorial properties of the boolean function. Our first result is a tight lower bound of Ω(log n) on the degree needed to represent any boolean function that epends on n variables. Our second result states that for every boolean function f the following measures are all polynomi-ally related: The decision tree complexity of f. The degree of the polynomial representing f. The smallest degree of a polynomial approximating f in the Lmax norm.

Original languageAmerican English
Title of host publicationProceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992
PublisherAssociation for Computing Machinery
Pages462-467
Number of pages6
ISBN (Electronic)0897915119
DOIs
StatePublished - 1 Jul 1992
Event24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada
Duration: 4 May 19926 May 1992

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129722
ISSN (Print)0737-8017

Conference

Conference24th Annual ACM Symposium on Theory of Computing, STOC 1992
Country/TerritoryCanada
CityVictoria
Period4/05/926/05/92

Bibliographical note

Publisher Copyright:
© 1992 ACM.

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