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Classical recursion theory
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Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.Abstract:
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.read more
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Elementarily computable functions over the real numbers and R-sub-recursive functions
Olivier Bournez,Emmanuel Hainry +1 more
TL;DR: It is proved that the Grzegorczyk Hierarchy functions correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema.
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Relativizations of randomness and genericity notions
TL;DR: In this article, the notion of Schnorr randomness was introduced and a base for weak 1-genericity was defined, where the halting set K is not Turing reducible to A.
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Enumerations of the Kolmogorov Function
Richard Beigel,Harry Buhrman,Peter A. Fejer,Lance Fortnow,Piotr Grabowski,Luc Longpré,Andrei A. Muchnik,Frank Stephan,Leen Torenvliet +8 more
TL;DR: In this article, a recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), and f is a k(n)-enumerator if for every input x of length n.
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Effective Search Problems
Martin Kummer,Frank Stephan +1 more
TL;DR: This work asks for the minimal number that can be achieved by a suitable choice of X and calls this quantity the query complexity of F, and introduces a fault tolerant version and relates it with Ulam's game.
Journal ArticleDOI
On the Turing Degrees of Weakly Computable Real Numbers
TL;DR: This paper discusses some basic degree properties of semi-computable and weakly computable real numbers introduced by Weihrauch and Zheng and shows that, there are two real numbers of c.c.e. binary expansions such that their difference does not have an ω.