The complexity of Boolean functions
The complexity of Boolean functions
Improved upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
A lower bound for integer greatest common divisor computations
Journal of the ACM (JACM)
Lower bounds for arithmetic problems
Information Processing Letters
Lower bounds for computations with the floor operation
SIAM Journal on Computing
Polynomial threshold functions, AC0 functions, and spectral norms
SIAM Journal on Computing
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Representing Boolean functions as polynomials modulo composite numbers
Computational Complexity - Special issue on circuit complexity
Lower Bounds on Representing Boolean Functions as Polynomials in $z_{m}$
SIAM Journal on Discrete Mathematics
A lower bound on the MOD 6 degree of the or function
Computational Complexity
A complex-number fourier technique for lower bounds on the mod-m degree
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
On computing Boolean functions by sparse real polynomials
FOCS '95 Proceedings of the 36th 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
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We say a polynomial P over ZM strongly M-represents a Boolean function F if F(x) ≡ P(x) (mod M) for all x ∈ {0, 1}n. Similarly, P one-sidedly M-represents F if F(x) = 0 ⇔ P(x) ≡ 0 (mod M) for all x ∈ {0, 1}n. Lower bounds are obtained on the degree and the number of monomials of polynomials over ZM, which strongly or one-sidedly M-represent the Boolean function deciding if a given n- bit integer is square-free. Similar lower bounds are also obtained for polynomials over the reals which provide a threshold representation of the above Boolean function.