Martin Ziegler

Non-Uniformly Computable Analysis

Abstract (html):
Recursive Analysis is often critisized for its 'Main Theorem',
ruling out as computable even the simplest discontinuous functions.
On the other hand many such functions do map computable arguments <i>x</i>
to computable values; and become computable when given, in addition
to <i>x</i>, some 'small' discrete advice. <br>
We recall some classical
examples and report on new ones. They suggest an information-theoretic
(and numerically reasonable) investigation on the minimum size (#bits)
of the aforementioned additional advice sufficient for
computability of the function under consideration.