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.
/lp/association-for-computing-machinery/guest-column-correlation-bounds-for-polynomials-over-0-1-yzK6019XIS