Dispersers, deterministic amplification, and weak random sources

The use of highly expanding bipartite multigraphs (called dispersers) to reduce greatly the error of probabilistic algorithms at the cost of few additional random bits is treated. Explicit constructions of such graphs are generalized and used to obtain the following results: (1) The error probability of any RP (BPP) algorithm can be made exponentially small at the cost of only a constant factor increase in the number of random bits. (2) RP (BPP) algorithms with some weak bit fixing sources are simulated