We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround communication protocols. Our proofs use the notion of information cost of a p...
We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i.) to show how open questions in algebraic complexity theory are naturally pose...
Given an algebraic number field K, such that [K : Q] is constant, we show that the problem of computing the units group O∗ K is in the complexity class SPP. As a consequence, w...
A Direct Sum Theorem holds in a model of computation, when for every problem solving some k input instances together is k times as expensive as solving one. We show that Direct Su...
Abstract. In recent years we have witnessed the proliferation of semidefinite programming bounds in combinatorial optimization [1,5,8], quantum computing [9,2,3,6,4,16] and even in...