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TR08-073 | 4th August 2008 00:00

Structural complexity of AvgBPP


Authors: Dmitry Itsykson
Publication: 28th August 2008 19:35
Downloads: 1313


We study class AvgBPP that consists of distributional problems that can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP 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 AvgP=AvgBPP. Note that, while it is easy to construct a promise problem that is complete for promise-BPP, it is unknown whether BPP contains complete languages.

We also prove a time hierarchy theorem for AvgBPP (time hierarchy theorem is also unknown for BPP). We compare average-case classes with their classical (worst-case) counterparts and show that the inclusions are proper.

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