We introduce two new complexity measures for Boolean functions, which we name sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query com...
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has ap...
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of...
We exactly determine the formula size of the parity function. If n = 2 + k, where 0 ≤ k < 2 , then the formula size of parity on n bits is 2 (2 + 3k) = n2 + k2 − k2 . Khrap...
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,...