Guest Column

Abstract

This article is a unified treatment of the state-of-the-art on the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0 1 }. It discusses long-standing results and recent developments, related proof techniques, and connections with pseudorandom generators. It also suggests several research directions.

Untitled

“…The problem of showing a specific given function to have no non-trivial approximation by low-degree polynomials has been extensively investigated, since solutions to this problem have many applications in complexity (cf. discussion and references in [1,3,16], as well as an excellent survey by Viola on correlation bounds [15]). …”