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We use the connection between resource-bounded dimension and the online mistake-bound model of learning to show that the following classes have polynomial-time dimension zero. 1. The class of problems which reduce to nondense sets via a majority reduction. 2. The class of problems which reduce to nondense sets via an iterated reduction that composes a… (More)

This article extends and improves the work of Fortnow and Klivans [2009], who showed that if a circuit class C has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [Angluin 1988], then we have the lower bound EXP<sup>NP</sup> not C. We use entirely different techniques involving betting games… (More)

We study the structure of the polynomial-time complete sets for NP and PSPACE under strong nondeterministic polynomial-time reductions (SNP-reductions). We show the following results. • If NP contains a p-random language, then all polynomial-time complete sets for PSPACE are SNP-isomorphic. • If NP ∩ co-NP contains a p-random language, then all… (More)

We consider resource-bounded measure in double-exponential-time complexity classes. In contrast to complexity class separation translating downwards, we show that measure separation translates upwards. For example, µ p (NP) = 0 ⇒ µ e (NE) = 0 ⇒ µ exp (NEXP) = 0. We also show that if NE does not have e-measure 0, then the NP-machine hypothesis holds. We give… (More)

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