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March 2012 An incomplete set of shortest descriptions
Frank Stephan, Jason Teutsch
J. Symbolic Logic 77(1): 291-307 (March 2012). DOI: 10.2178/jsl/1327068704

Abstract

The truth-table degree of the set of shortest programs remains an outstanding problem in recursion theory. We examine two related sets, the set of shortest descriptions and the set of domain-random strings, and show that the truth-table degrees of these sets depend on the underlying acceptable numbering. We achieve some additional properties for the truth-table incomplete versions of these sets, namely retraceability and approximability. We give priority-free constructions of bounded truth-table chains and bounded truth-table antichains inside the truth-table complete degree by identifying an acceptable set of domain-random strings within each degree.

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Frank Stephan. Jason Teutsch. "An incomplete set of shortest descriptions." J. Symbolic Logic 77 (1) 291 - 307, March 2012. https://doi.org/10.2178/jsl/1327068704

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1245.03062
MathSciNet: MR2951642
Digital Object Identifier: 10.2178/jsl/1327068704

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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