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June 2013 Nonexistence of minimal pairs for generic computability
Gregory Igusa
J. Symbolic Logic 78(2): 511-522 (June 2013). DOI: 10.2178/jsl.7802090

Abstract

A generic computation of a subset $A$ of $\mathbb{N}$ consists of a computation that correctly computes most of the bits of $A$, and never incorrectly computes any bits of $A$, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic computability, answering a question of Jockusch and Schupp.

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Gregory Igusa. "Nonexistence of minimal pairs for generic computability." J. Symbolic Logic 78 (2) 511 - 522, June 2013. https://doi.org/10.2178/jsl.7802090

Information

Published: June 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1302.03048
MathSciNet: MR3145193
Digital Object Identifier: 10.2178/jsl.7802090

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 2 • June 2013
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