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References (16)
-
Achilles Beros (2013)
LEARNING THEORY IN THE ARITHMETIC HIERARCHYThe Journal of Symbolic Logic, 79
-
J. Case, Sanjay Jain, Arun Sharma (1996)
Anomalous Learning Helps SuccinctnessTheor. Comput. Sci., 164
-
E. Gold (1967)
Language Identification in the LimitInf. Control., 10
-
L. Blum, M. Blum (1975)
Toward a Mathematical Theory of Inductive InferenceInf. Control., 28
-
S. Kapur, G. Bilardi (1992)
On Uniform Learnability of Language FamiliesInf. Process. Lett., 44
-
L. Carlucci, J. Case, Sanjay Jain, F. Stephan (2008)
Non-U-shaped vacillatory and team learningJ. Comput. Syst. Sci., 74
-
L. Carlucci, J. Case, Sanjay Jain, F. Stephan (2005)
Non U-Shaped Vacillatory and Team Learning -
Ganesh Baliga, J. Case, Sanjay Jain (1999)
The Synthesis of Language LearnersInf. Comput., 152
-
R. Soare (1987)
Recursively enumerable sets and degrees - a study of computable functions and computability generated sets -
Achilles Beros (2009)
Anomalous Vacillatory LearningThe Journal of Symbolic Logic, 78
-
A Sharma (1999)
Systems That Learn: An Introduction to learning Theory -
L. Carlucci (2005)
Non U-shaped vacillatory and team learning. In: International Conference on Algorithmic Learning TheoryInternational Conference on Algorithmic Learning Theory
-
M. Kummer, F. Stephan (1993)
On the structure of degrees of inferabilityJ. Comput. Syst. Sci., 52
-
D. Osherson, M. Stob, S. Weinstein (1990)
Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists -
J. Case (1999)
The Power of Vacillation in Language LearningSIAM J. Comput., 28
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2020
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-020-00745-4
- Publisher site
- See Article on Publisher Site
Abstract
The present work determines the arithmetic complexity of the index sets of u.c.e. families which are learnable according to various criteria of algorithmic learning. Specifically, we prove that the index set of codes for families that are TxtFexba\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^a_b$$\end{document}-learnable is Σ40\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Sigma _4^0$$\end{document}-complete and that the index set of TxtFex∗∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^*_*$$\end{document}-learnable and the index set of TxtFext∗∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^*_*$$\end{document}-learnable families are both Σ50\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Sigma _5^0$$\end{document}-complete.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Aug 26, 2020