Proceedings ArticleDOI
Turing degrees and the ershov hierarchy
Frank Stephan,Yue Yang,Liang Yu +2 more
- pp 300-321
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The early work by Ershov and others on this hierarchy and the most fundamental results are surveyed and some pointers to concurrent work in the field are provided.Abstract:
An n-r.e. set can be defined as the symmetric difference of n recursively enumerable sets. The classes of these sets form a natural hierarchy which became a well-studied topic in recursion theory. In a series of ground-breaking papers, Ershov generalized this hierarchy to transfinite levels based on Kleene’s notations of ordinals and this work lead to a fruitful study of these sets and their many-one and Turing degrees. The Ershov hierarchy is a natural measure of complexity of the sets below the halting problem. In this paper, we survey the early work by Ershov and others on this hierarchy and present the most fundamental results. We also provide some pointers to concurrent work in the field.read more
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References
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Journal ArticleDOI
Theory of Recursive Functions and Effective Computability.
Solomon Feferman,Hartley Rogers +1 more
TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.
Journal ArticleDOI
Language identification in the limit
TL;DR: It was found that theclass of context-sensitive languages is learnable from an informant, but that not even the class of regular languages is learningable from a text.
Book
Systems That Learn: An Introduction to Learning Theory
TL;DR: Systems That Learn presents a mathematical framework for the study of learning in a variety of domains that provides the basic concepts and techniques of learning theory as well as a comprehensive account of what is currently known about a range of learning paradigms.
Book
Higher recursion theory
TL;DR: In this article, hyperarithmetic theory is developed at length and used to lift classical recursion theory from integers to recursive ordinals (metarecursion) and two further liftings are then made, first ordinals and then sets (E-recursion).
Book
Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists
TL;DR: Systems that learn as discussed by the authors is a mathematical framework for the study of learning in a variety of domains and provides the basic concepts and techniques of learning theory as well as a comprehensive account of what is currently known about learning paradigms.