Noam Nisan Mario Szegedy December 1, 1994  Home/Search
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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\Omega\Gamma/33 n) on the degree needed to represent any boolean function that depends on n variables. Our second result states that for every boolean function f the following measures are all polynomially related: ffl The decision tree complexity of f .... (Update)
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BibTeX entry: (Update)
N. Nisan and M. Szegedy. On the degree of boolean functions as real polynomial. In Proceedings of the 24th ACM Symposium on the Theory of Computing, pages 462--467. ACM, New York, 1992. http://citeseer.ist.psu.edu/nisan92degree.html More
@inproceedings{ nisan92degree,
author = "Noam Nisan and Mario Szegedy",
title = "On the degree of {Boolean} functions as real polynomials",
pages = "462--467",
year = "1992",
url = "citeseer.ist.psu.edu/nisan92degree.html" }
Citations (may not include all citations):202 The complexity of Boolean functions - Wegener - 1987
149 Fast probabilistic Algorithms for verification of Polynomial.. (context) - Schwartz - 1980
103 Introduction to approximation theory (context) - Cheney - 1966
59 The influence of variables on boolean functions (context) - Kahn, Kalai et al. - 1988
51 Lower bounds for the size of circuits of bounded depth with .. (context) - Razborov - 1987
32 Fourier transform and Learnability (context) - Linial, Mansour et al. - 1989
16 Schwankung von Polynomen zwischen Gitterpunkten (context) - Ehlich, Zeller - 1964
11 A comparison of Uniform Approximations on an interval and a .. (context) - Rivlin, Cheney - 1966
8 Exact Time Bounds for Computing Boolean Functions on PRAMs W.. (context) - Dietzfelbinger, Kutylowski et al. - 1990
6 Technical report YALEU/DCS/TR (context) - Beigel, Reingold et al. - 1990
5 CREW PRAM's and decision trees (context) - Nisan - 1989
3 Learning decision trees using the Fourier transform (context) - Kushilevitz, Mansour - 1991
1 the expressive power of voting polynomials (context) - Aspens, Beigel et al. - 1991
1 Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolenski - 1987
1 AC 0 functions and spectral norms (context) - Brook, Smolenski et al. - 1990
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