In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of ...
In this paper, Boolean functions in ,4C0 are studied using harmonic analysis on the cube. The main result is that an ACO Boolean function has almost all of its “power spectrum”...
—We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most O(k3 log d). The previous best rank bound known was 2O(k2 ) (log d)k−2...
We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f : {0, 1}l → {0, 1} ...
Division is a fundamental problem for arithmetic and algebraic computation. This paper describes Boolean circuits of bounded fan-in for integer division nding reciprocals that...