Note: Not every domain of a plain decompressor contains the domain of a prefix-free one

Authors:
Mikhail Andreev;Ilya Razenshteyn;Alexander Shen
Affiliations:
Mathematics Department, Moscow State University, Vorobyovy Gory, Moscow, 119899, Russia;Mathematics Department, Moscow State University, Vorobyovy Gory, Moscow, 119899, Russia;LIF, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, F-13453, Marseille, Cedex13, France
Venue:
Theoretical Computer Science
Year:
2011

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Universal Recursively Enumerable Sets of Strings

DLT '08 Proceedings of the 12th international conference on Developments in Language Theory

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Abstract

C. Calude, A. Nies, L. Staiger, and F. Stephan posed the following question about the relation between plain and prefix Kolmogorov complexities (see their paper in DLT 2008 conference proceedings): does the domain of every optimal decompressor contain the domain of some optimal prefix-free decompressor? In this paper we provide a negative answer to this question.