Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Logic and Foundations
Enumerations Of The Kolmogorov Function, Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet
Enumerations Of The Kolmogorov Function, Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet
Peter Fejer
A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x). f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A.
We determine exactly how hard it is to enumerate the Kolmogorov function, which assigns to each string x its Kolmogorov complexity:
- For every underlying universal machine U, there is a constant a …