We study the compression of polynomially samplable sources. In particular, we give efficient prefix-free compression and decompression algorithms for three classes of such sources (whose support is a subset of {0,1}^n).

1. We show how to compress sources X samplable by logspace machines to expected length H(X)+O(1).

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We prove that every language in $\mathrm{P}^{\# \mathrm{P}}$ can be decided by a bounded-error randomized algorithm that uses only $O(\log n)$ bits of work space. The algorithm is guaranteed to halt for every input and every setting of the random tape. However, there is a catch: the algorithm uses a ... more >>>