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Enumerations of the Kolmogorov function

Published online by Cambridge University Press:  12 March 2014

Richard Beigel
Affiliation:
Department of Computer and Information Sciences, Temple University, 1805 North Broad Street, Philadelphia PA 19122, USA. E-mail: beigel@cis.temple.edu
Harry Buhrman
Affiliation:
Centrum Voor Wiskunde en Informatica (CWI), Kruislaan 413, 1090 GB Amsterdam, The Netherlands. E-mail: buhrman@cwi.nl
Peter Fejer
Affiliation:
Department of Computer Science, University of Massachusetts Boston, Boston, MA 02125, USA. E-mail: fejer@cs.umb.edu
Lance Fortnow
Affiliation:
Department of Computer Science, University of Chicago, 1100 East 58TH Street, Chicago, IL 60637, USA. E-mail: fortnow@cs.uchicago.edu
Piotr Grabowski
Affiliation:
Institut für Informatik, Im Neuenheimer Feld 294. 69120 Heidelberg, Germany. E-mail: pgrabows@ix.urz.uni-heidelberg.de
Luc Longpré
Affiliation:
University of Texasat el Paso, El Paso, TX 79968, USA. E-mail: longpre@utep.edu
Andrej Muchnik
Affiliation:
Institute of New Techologies, Nizhnyaya Radishevskaya, 10. Moscow, 109004, Russia. E-mail: muchnik@lpcs.math.msu.ru
Frank Stephan
Affiliation:
School of Computing and Department of Mathematics, National University of Singapore, 3 Science Drive 2, Singapore 117543., Republic of Singapore. E-mail: fstephan@comp.nus.edu.sg
Leen Torenvliet
Affiliation:
Institute for Language, Logic and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam

Abstract

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x). f is a k(n)-enumerator if for every input x of length n. h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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