Section: New Results

Extension of computable functions

Participant : Mathieu Hoyrup.

We worked on the computable aspects of an elementary problem in real analysis: extending a continuous function on a larger domain. More precisely, if a real-valued function $f$ is defined on an interval $[0,a)$ (with $0<a<1$) and is computable there, under which conditions can it be extended to a computable function on $[0,1]$? Although this question has a very simple formulation, it does not have a simple answer. We obtained many results showing how the answer depends on $a$ and on the way $f$ converges at $a$. Surprisingly, this problem provides new characterizations of already existing classes of real numbers previously defined in computability theory. This work is joint with Walid Gomaa and has been presented at LICS 2017 [19].