Pseudorandomness for Permutation Branching Programs Without the Group Theory

The typical way we derandomize a randomized computation is to replace the truly random bits used by the computation with suitable pseudorandom bits. We require that using pseudorandom, rather than truly random, bits does not change the output of the computation with probability more than ε; we call this parameter the error. The algorithm that produces the pseudorandom bits is called a pseudorandom generator and the number of random bits needed by this algorithm to sample the distribution is called the seed length. The pseudorandom generator needs to be efficiently computable and the seed length needs to be short enough for all possible seeds to be enumerated in a deterministic simulation.