Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The complexity of Boolean functions
The complexity of Boolean functions
On the influence of single participant in coin flipping schemes
SIAM Journal on Discrete Mathematics
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Exact time bounds for computing boolean functions on PRAMs without simultaneous writes
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
The expressive power of voting polynomials
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Learning decision trees using the Fourier spectrum
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Exact lower time bounds for computing Boolean functions on CREW PRAMs
Journal of Computer and System Sciences
Pseudorandom generators and learning algorithms for AC
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A theorem on sensitivity and applications in private computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
New degree bounds for polynomial threshold functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Regular Languages are Testable with a Constant Number of Queries
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Log-Rank conjecture and low degree polynomials
Information Processing Letters
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Every decision tree has an in.uential variable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Quantum communication complexity of block-composed functions
Quantum Information & Computation
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
Lower Bounds for Randomized Exclusive Write PRAMs
Theory of Computing Systems
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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 &OHgr;(log 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:(1) The decision tree complexity of f. (2) The degree of the polynomial representing f. (3) The smallest degree of a polynomial approximating f in the Lmax norm.