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LEARNING THEORY IN THE ARITHMETIC HIERARCHY

  • ACHILLES A. BEROS (a1)

Abstract

We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning, learning in the limit, behaviorally correct learning and anomalous learning in the limit. In proving the ${\rm{\Sigma }}_5^0$ -completeness result for behaviorally correct learning we prove a result of independent interest; if a uniformly computably enumerable family is not learnable, then for any computable learner there is a ${\rm{\Delta }}_2^0$ enumeration witnessing failure.

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[1]Angluin, Dana, Inductive inference of formal languages from positive data. Information and Control, vol. 45 (1980), pp. 117135.
[2]Bārzdiņš, Janis, Two theorems on the limit synthesis of functions. Theory of Algorithm and Programs, vol. 1 (1974), pp. 8288.
[3]Bārzdiņš, Janis and Freivalds, Rūsiņš, Prediction of general recursive functions. Doklady Akademii Nauk SSSR, vol. 206 (1972), pp. 521524.
[4]Blum, Lenore and Blum, Manuel, Toward a mathematical theory of inductive inference. Information and Control, vol. 28 (1975), pp. 125155.
[5]Gold, Mark, Language identification in the limit, Information and Control, vol. 10 (1967), pp. 447474.
[6]Osherson, Daniel, Stob, Michael, and Weinstein, Scott, Systems that learn: An introduction to learning theory for cognitive and computer scientists, MIT Press, Cambridge, MA, 1986.
[7]Osherson, Daniel and Weinstein, Scott, Criteria of language learning, Information and Control, vol. 52 (1982), pp. 123138.
[8]Soare, Robert I., Recursively enumerable sets and degrees: A study of computable functions and computably generated sets, Springer-Verlag, Berlin, Heidelberg, 1987.

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