Pseudorandom generators for space-bounded computation

Pseudorandom generators are constructed which convert O(Slog R) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slog n) random bits. An application of these generators is an explicit construction of universal traversal sequences (for arbitrary graphs) of length n^{O(log n)}. The generators constructed are technically stronger than just appearing random to spacebounded machines, and have several other applications. In particular, applications are given for "deterministic amplification" (i.e. reducing the probability of error of randomized algorithms), as well as generalizations of it.