Ryan C. Harkins

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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&#8217;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, μp(NP) 6= 0⇒ μe(NE) 6= 0⇒ μexp(NEXP) 6= 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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