Nearly optimal language compression using extractors

Abstract

We show two sets of results applying the theory of extractors to resource-bounded Kolmogorov complexity: - Most strings in easy sets have nearly optimal polynomial-time CD complexity. This extends work of Sipser [Sip83] and Buhrman and Fortnow [BF97]. - We use extractors to extract the randomness of strings. In particular we show how to get from an arbitrary string, an incompressible string which encodes almost as much polynomial-time CND complexity as the original string. © 1998 Springer-Verlag.