The complexity of Boolean functions
The complexity of Boolean functions
A Spectral Lower Bound Technique for the Size of Decision Trees and Two-Level AND/OR Circuits
IEEE Transactions on Computers
Improved upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Measures of Boolean function complexity based on harmonic analysis
CIAC '94 Proceedings of the second Italian conference on Algorithms and complexity
An exponential lower bound for depth 3 arithmetic circuits
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The average sensitivity of bounded-depth circuits
Information Processing Letters
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
On the Complexity of Balanced Boolean Functions
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
On Polynomial Representations of Boolean Functions Related to Some Number Theoretic Problems
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Complexity of some arithmetic problems for binary polynomials
Computational Complexity
On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
Bounds on the Fourier coefficients of the weighted sum function
Information Processing Letters
On the Optimality of the Binary Algorithm for the Jacobi Symbol
Fundamenta Informaticae
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We extend the area of applications of the Abstract Harmonic Analysis to lower bounds on the circuit and decision tree complexity of Boolean functions related to some number theoretic problems. In particular, we prove that deciding if a given integer is square-free and testing co-primality of two integers by unbounded fan-in circuits of bounded depth requires superpolynomial size. Copyright 2001 Academic Press.