Prefix-Like Complexities and Computability in the Limit
- Cite this paper as:
- Chernov A., Schmidhuber J. (2006) Prefix-Like Complexities and Computability in the Limit. In: Beckmann A., Berger U., Löwe B., Tucker J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg
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.
KeywordsKolmogorov complexity limit computability generalized Turing machine non-halting computation
Unable to display preview. Download preview PDF.