On the degree of boolean functions as real polynomials
- Noam NisanAffiliated withThe Hebrew University
- , Mario SzegedyAffiliated withAT & T Bell Laboratories
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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(logn) on the degree needed to represent any Boolean function that depends onn variables.
o The decision tree complexity off.
o The degree of the polynomial representingf.
o The smallest degree of a polynomialapproximating f in theL max norm.
Key wordsApproximation block sensitivity Boolean functions Fourier degree
Subject classifications68Q05 68Q99
- On the degree of boolean functions as real polynomials
Volume 4, Issue 4 , pp 301-313
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- block sensitivity
- Boolean functions
- Fourier degree
- Industry Sectors