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» Undecidability in Weihrauch Degrees
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CIE
2010
Springer
13 years 5 months ago
Undecidability in Weihrauch Degrees
Oleg V. Kudinov, Victor L. Selivanov, Anton V. Zhu...
CCA
2009
Springer
14 years 5 months ago
Weihrauch Degrees, Omniscience Principles and Weak Computability
Abstract. In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension of this reducibility for multi-valued functions ...
Vasco Brattka, Guido Gherardi
JC
2000
89views more  JC 2000»
13 years 10 months ago
Weakly Computable Real Numbers
The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. In this paper we discuss some basic degr...
Klaus Ambos-Spies, Klaus Weihrauch, Xizhong Zheng
CCA
2009
Springer
14 years 2 months ago
Effective Choice and Boundedness Principles in Computable Analysis
Abstract. In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can...
Vasco Brattka, Guido Gherardi
JCSS
2007
75views more  JCSS 2007»
13 years 10 months ago
Undecidability of the structure of the Solovay degrees of c.e. reals
We show that the elementary theory of the structure of the Solovay degrees of computably enumerable reals is undecidable.
Rodney G. Downey, Denis R. Hirschfeldt, Geoffrey L...