We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input,...
Abstract. We consider dynamic evaluation of algebraic functions (matrix multiplication, determinant, convolution, Fourier transform, etc.) in the model of Reif and Tate; i.e., if f...
Gudmund Skovbjerg Frandsen, Johan P. Hansen, Peter...
We prove that the concept class of disjunctions cannot be pointwise approximated by linear combinations of any small set of arbitrary real-valued functions. That is, suppose there ...
We prove exponential lower bounds for the refutation of a random 3-CNF with linear number of clauses by k-DNF Resolution for k log n/ log log n. For this we design a specially ta...
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...