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On universal computably enumerable prefix codes

Published online by Cambridge University Press:  01 February 2009

CRISTIAN S. CALUDE  and
LUDWIG STAIGER
CRISTIAN S. CALUDE
Affiliation:
Department of Computer Science, The University of Auckland, Private Bag 92019, Auckland, New Zealand Email: cristian@cs.auckland.ac.nz
LUDWIG STAIGER
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, Institut für Informatik, D - 06099 Halle, Germany Email: staiger@informatik.uni-halle.de
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Abstract

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We study computably enumerable (c.e.) prefix codes that are capable of coding all positive integers in an optimal way up to a fixed constant: these codes will be called universal. We prove various characterisations of these codes, including the following one: a c.e. prefix code is universal if and only if it contains the domain of a universal self-delimiting Turing machine. Finally, we study various properties of these codes from the points of view of computability, maximality and density.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Special Issue 1: Theory and Applications of Models of Computation (TAMC) , February 2009 , pp. 45 - 57
Copyright
Copyright © Cambridge University Press 2009

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