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53
Turing degrees of hypersimple relations on computable Structures, submitted to Annals of Pure and Applied Logic
"... Abstract. Let A be an infinite computable structure, and let R be an additional computable relation on its domain A. Thesyntactic notion of formal hypersimplicity of R on A, first introduced and studied by G. Hird, is analogous to the computabilitytheoretic notion of hypersimplicity of R on A, give ..."
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Cited by 1 (0 self)
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Classification: 03C57, 03D45 Keywords: computable structure, hypersimple relation, Turing degree
On the uniform learnability of approximations to nonrecursive functions
 Algorithmic Learning Theory: Tenth International Conference (ALT 1999), volume 1720 of Lecture Notes in Artificial Intelligence
, 1999
"... Abstract. Blum and Blum (1975) showed that a class B of suitable recursive approximations to the halting problem is reliably EXlearnable. These investigations are carried on by showing that B is neither in NUM nor robustly EXlearnable. Since the definition of the class B is quite natural and does ..."
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Cited by 5 (3 self)
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corresponding function classes U(A) are still EXinferable but may fail to be reliably EXlearnable, for example if A is nonhigh and hypersimple. Additionally, it is proved that U(A) is neither in NUM nor robustly EXlearnable provided A is part of a recursively inseparable pair, A is simple
Learning Classes of Approximations to NonRecursive Functions
 Theoret. Comput. Sci
"... Blum and Blum (1975) showed that a class B of suitable recursive approximations to the halting problem K is reliably EXlearnable but left it open whether or not B is in NUM . By showing B to be not in NUM we resolve this old problem. Moreover, variants of this problem obtained by approximating any ..."
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Cited by 3 (3 self)
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any given recursively enumerable set A instead of the halting problem K are studied. All corresponding function classes U(A) are still EXinferable but may fail to be reliably EXlearnable, for example if A is nonhigh and hypersimple. Blum and Blum (1975) considered only approximations to K defined
Computational Processes and Incompleteness
, 906
"... We introduce a formal definition of Wolfram’s notion of computational process based on cellular automata, a physicslike model of computation. There is a natural classification of these processes into decidable, intermediate and complete. It is shown that in the context of standard finite injury pri ..."
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We introduce a formal definition of Wolfram’s notion of computational process based on cellular automata, a physicslike model of computation. There is a natural classification of these processes into decidable, intermediate and complete. It is shown that in the context of standard finite injury
Codable Sets and Orbits of Computably Enumerable Sets
 J. Symbolic Logic
, 1995
"... A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let E denote the structure of the computably enumerable sets under inclusion, E = (fW e g e2! ; `). We previously exhibited a first order ..."
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Cited by 12 (5 self)
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A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let E denote the structure of the computably enumerable sets under inclusion, E = (fW e g e2! ; `). We previously exhibited a first
 [2485].Approximation [2560].
, 2011
"... Version 1.21 Title word crossreference 1, 579 n [827]. 16 [2096]. 2 [941]. 2/3 [2560]. 3 [567]. AC O [252]. mod2 32 [91]. C ∗ ∗ [2435]. d [1690]. E 3 [2352]. f [2550]. Fω [198]. GeO2 [1528]. k [774]. l [2103]. m [1359]. AC 0 [1007]. TLA + [1979]. N [535]. N × M [1932]. O(1) [2555]. O(log log n) [73 ..."
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Version 1.21 Title word crossreference 1, 579 n [827]. 16 [2096]. 2 [941]. 2/3 [2560]. 3 [567]. AC O [252]. mod2 32 [91]. C ∗ ∗ [2435]. d [1690]. E 3 [2352]. f [2550]. Fω [198]. GeO2 [1528]. k [774]. l [2103]. m [1359]. AC 0 [1007]. TLA + [1979]. N [535]. N × M [1932]. O(1) [2555]. O(log log n
Recursion Theory
"... Recursion theory deals with the fundamental concepts on what subsets of natural numbers (or other famous countable domains) could be defined effectively and how complex the so defined sets are. The basic concept are the recursive and recursively enumerable sets, but the world of sets investigated in ..."
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Recursion theory deals with the fundamental concepts on what subsets of natural numbers (or other famous countable domains) could be defined effectively and how complex the so defined sets are. The basic concept are the recursive and recursively enumerable sets, but the world of sets investigated in recursion theory goes beyond these sets. The notions are linked to Diophantine sets, definability by functions via recursion and Turing machines. Although some of the concepts are very old, it took until Matiyasevich’s great result that Diophantine and r.e. sets are the same that the picture was fully understood. This lecture gives an overview on the basic results and proof methods in recursion theory.
on the lecture “Recursion Theory ” and its syllabus. Furthermore, he wants to thank
"... Recursion theory deals with the fundamental concepts on what subsets of natural numbers (or other famous countable domains) could be defined effectively and how complex the so defined sets are. The basic concept are the recursive and recursively enumerable sets, but the world of sets investigated in ..."
Abstract
 Add to MetaCart
Recursion theory deals with the fundamental concepts on what subsets of natural numbers (or other famous countable domains) could be defined effectively and how complex the so defined sets are. The basic concept are the recursive and recursively enumerable sets, but the world of sets investigated in recursion theory goes beyond these sets. The notions are linked to Diophantine sets, definability by functions via recursion and Turing machines. Although some of the concepts are very old, it took until Matiyasevich’s great result that Diophantine and r.e. sets are the same that the picture was fully understood. This lecture gives an overview on the basic results and proof methods in recursion theory.
Results 1  10
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53