The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bo...
Abstract-- Given a family of real or complex monic polynomials of fixed degree with one fixed affine constraint on their coefficients, consider the problem of minimizing the root r...
Vincent D. Blondel, Mert Gurbuzbalaban, Alexandre ...
We show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) field and that the same holds true for functional tranducers as well....
Abstract. Motivated by juggling sequences and bubble sort, we examine permutations on the set {1, 2, . . . , n} with d descents and maximum drop size k. We give explicit formulas f...
Fan R. K. Chung, Anders Claesson, Mark Dukes, Rona...
We discuss several complexity measures for Boolean functions: certi cate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. ...