Guest Column: A Paradigm for Arithmetic Circuit Lower Bounds

Abstract

How many operations are needed to compute a given polynomial f(x1; x2; : : : ; xn)? Answering questions of this form naturally leads us on a search for clever algorithmic techniques to reduce the number of operations required. Simultaneously, it also leads us towards the complementary task of finding techniques and paradigms for proving lower bounds on the minimum number of operations required. In this survey we describe one such paradigm for obtaining lower bounds.