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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 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)

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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