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On randomized counting versus randomised decision

Published 5 Jan 2018 in cs.CC | (1801.01901v1)

Abstract: We study the question of which counting problems admit f.p.r.a.s., under a structural complexity perspective. Since problems in #P with NP-complete decision version do not admit f.p.r.a.s. (unless NP = RP), we study subclasses of #P, having decision version either in P or in RP. We explore inclusions between these subclasses and we present all possible worlds with respect to NP v.s. RP and RP v.s. P.

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