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Complexity for partial computable functions over computable Polish spaces

Published online by Cambridge University Press:  19 December 2016

MARGARITA KOROVINA  and
OLEG KUDINOV
MARGARITA KOROVINA
Affiliation:
A.P. Ershov Institute of Informatics systems, NSU, Novosibirsk, Russia Email: rita.korovina@gmail.com
OLEG KUDINOV
Affiliation:
Sobolev Institute of Mathematics, NSU, Novosibirsk, Russia Email: kud@math.nsc.ru
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Abstract

In the framework of effectively enumerable topological spaces, we introduce the notion of a partial computable function. We show that the class of partial computable functions is closed under composition, and the real-valued partial computable functions defined on a computable Polish space have a principal computable numbering. With respect to the principal computable numbering of the real-valued partial computable functions, we investigate complexity of important problems such as totality and root verification. It turns out that for some problems the corresponding complexity does not depend on the choice of a computable Polish space, whereas for other ones the corresponding choice plays a crucial role.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 3: Mind, Mechanism and Mathematics: Computability Unchained , March 2018 , pp. 429 - 447
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Copyright © Cambridge University Press 2016 

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