We say a polynomial P over ZZM 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 ⇐...
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hype...
In this paper we study the degree of non-constant symmetric functions f : {0, 1}n → {0, 1, . . . , c}, where c ∈ N, when represented as polynomials over the real numbers. We s...
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolm...
We develop a new method for estimating the discrepancy of tensors associated with multiparty communication problems in the “Number on the Forehead” model of Chandra, Furst and...