TL;DR: This work shows how to get from an arbitrary string, an incompressible string which encodes almost as much polynomial-time CND complexity as the original string.
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.
TL;DR: A constructive topological analysis of the “size” of the set of random strings is developed in order to show to what extent they are incompressible.