Prefix-Like complexities and computability in the limit

Authors:
Alexey Chernov;Jürgen Schmidhuber
Affiliations:
IDSIA, Manno, Switzerland;IDSIA, Manno, Switzerland
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

Citing 11
Cited 0

On learning limiting programs

COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
A Theory of Program Size Formally Identical to Information Theory

Journal of the ACM (JACM)
Descriptive complexity of computable sequences

Theoretical Computer Science
Coins, Quantum Measurements, and Turing's Barrier

Quantum Information Processing
Functions Computable in the Limit by Probabilistic Machines

Proceedings of the 3rd Symposium on Mathematical Foundations of Computer Science
Towards Limit Computable Mathematics

TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Algorithmic Theories of Everything

Algorithmic Theories of Everything
A coding theorem for enumerable output machines

Information Processing Letters
Kolmogorov Complexity for Possibly Infinite Computations

Journal of Logic, Language and Information
Noisy turing machines

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming

Quantified Score

Hi-index	0.00

Visualization

Abstract

Computability in the limit represents the non-plus-ultra of constructive describability. It is well known that the limit computable functions on naturals are exactly those computable with the oracle for the halting problem. However, prefix (Kolmogorov) complexities defined with respect to these two models may differ. We introduce and compare several natural variations of prefix complexity definitions based on generalized Turing machines embodying the idea of limit computability, as well as complexities based on oracle machines, for both finite and infinite sequences.