On the degree of boolean functions as real polynomials

Noam Nisan; Mario Szegedy

doi:10.1145/129712.129757

On the degree of boolean functions as real polynomials

Noam Nisan
, Mario Szegedy

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

54 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 L_max norm.

Original language	English
Title of host publication	Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992
Publisher	Association for Computing Machinery
Pages	462-467
Number of pages	6
ISBN (Electronic)	0897915119
DOIs	https://doi.org/10.1145/129712.129757
State	Published - 1 Jul 1992
Event	24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada Duration: 4 May 1992 → 6 May 1992

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F129722
ISSN (Print)	0737-8017

Conference

Conference	24th Annual ACM Symposium on Theory of Computing, STOC 1992
Country/Territory	Canada
City	Victoria
Period	4/05/92 → 6/05/92

Bibliographical note

Publisher Copyright:
© 1992 ACM.

Access to Document

10.1145/129712.129757

Cite this

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Nisan, N & Szegedy, M 1992, On the degree of boolean functions as real polynomials. in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F129722, Association for Computing Machinery, pp. 462-467, 24th Annual ACM Symposium on Theory of Computing, STOC 1992, Victoria, Canada, 4/05/92. https://doi.org/10.1145/129712.129757

On the degree of boolean functions as real polynomials. / Nisan, Noam; Szegedy, Mario.
Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992. Association for Computing Machinery, 1992. p. 462-467 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129722).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On the degree of boolean functions as real polynomials

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