Applications of Derandomization Theory in Coding: A Dissertation

Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate or reduce the need for randomness in such randomized constructions. Towards this goal, numerous fundamental notions have been developed to provide a unified framework for approaching various derandomization problems and to improve our general understanding of the power of randomness in computation. Two important classes of such tools are pseudorandom generators and randomness extractors. Pseudorandom generators transform a short, purely random, sequence into a much longer sequence that looks random, while extractors transform a weak source of randomness into a perfectly random one (or one with much better qualities, in which case the transformation is called a randomness condenser ).