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
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Improved upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
A course in computational algebraic number theory
A course in computational algebraic number theory
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Algorithmic number theory
The average sensitivity of bounded-depth circuits
Information Processing Letters
Modern computer algebra
On P versus NP CO-NP for decision trees and read-once branching programs
Computational Complexity
The average sensitivity of square-freeness
Computational Complexity
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Circuit and decision tree complexity of some number theoretic problems
Information and Computation
Circuit complexity of testing square-free numbers
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the average sensitivity of testing square-free numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Constant-Depth circuits for arithmetic in finite fields of characteristic two
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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We study various combinatorial complexity measures of Boolean functions related to some natural arithmetic problems about binary polynomials, that is, polynomials over F2. In particular, we consider the Boolean function deciding whether a given polynomial over F2 is squarefree. We obtain an exponential lower bound on the size of a decision tree for this function, and derive an asymptotic formula, having a linear main term, for its average sensitivity. This allows us to estimate other complexity characteristics such as the formula size, the average decision tree depth and the degrees of exact and approximative polynomial representations of this function. Finally, using a different method, we show that testing squarefreeness and irreducibility of polynomials over F2 cannot be done in AC0[p] for any odd prime p. Similar results are obtained for deciding coprimality of two polynomials over F2 as well.