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On the extension of computable real functions

Mathieu Hoyrup 1 Walid Gomaa 2
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We investigate interrelationships among different notions from mathematical analysis, effective topology, and classical computability theory. Our main object of study is the class of computable functions defined over an interval with the boundary being a left-c.e. real number. We investigate necessary and sufficient conditions under which such functions can be computably extended. It turns out that this depends on the behavior of the function near the boundary as well as on the class of left-c.e. real numbers to which the boundary belongs, that is, how it can be constructed. Of particular interest a class of functions is investigated: sawtooth functions constructed from computable enumerations of c.e. sets.
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Submitted on : Thursday, March 23, 2017 - 11:29:25 AM
Last modification on : Thursday, October 10, 2019 - 3:04:03 PM
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Mathieu Hoyrup, Walid Gomaa. On the extension of computable real functions. Logic In Computer Science (LICS), Jun 2017, Reykjavik, Iceland. ⟨hal-01494332⟩

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