Annals of Pure and Applied Logic 162 (3):213-223 (2010)

Abstract
We study the class that consists of distributional problems which can be solved in average polynomial time by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for under polynomial time samplable distributions. Since we use deterministic reductions, the existence of a deterministic algorithm with average polynomial running time for our problem would imply. Note that, while it is easy to construct a promise problem that is complete for, it is unknown whether contains complete languages. We also prove a time hierarchy theorem for. We compare average-case classes with their classical counterparts and show that the inclusions are proper.
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DOI 10.1016/j.apal.2010.09.006
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