DROPS

Document

Natural Halting Probabilities, Partial Randomness, and Zeta Functions

Authors: Christian S. Calude and Michael A. Stay

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract

We introduce the {it natural halting probability} and the {it natural complexity} of a Turing machine and we relate them to program-size complexity and Chaitin's halting probability. A classification of Turing machines according to their natural (Omega) halting probabilities is proposed: divergent, convergent and tuatara. We prove the existence of universal convergent and tuatara machines. Various results on randomness and partial randomness are proved. For example, we show that the natural halting probability of a universal tuatara machine is c.e. and random. A new type of partial randomness, asymptotic randomness, is introduced. Finally we show that in contrast to classical (algorithmic) randomness---which cannot be characterised in terms of plain complexity---various types of partial randomness admit such characterisations.

Cite as

Christian S. Calude and Michael A. Stay. Natural Halting Probabilities, Partial Randomness, and Zeta Functions. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

Copy BibTex To Clipboard

@InProceedings{calude_et_al:DagSemProc.06051.10,
  author =	{Calude, Christian S. and Stay, Michael A.},
  title =	{{Natural Halting Probabilities, Partial Randomness, and Zeta Functions}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--1},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.10},
  URN =		{urn:nbn:de:0030-drops-6319},
  doi =		{10.4230/DagSemProc.06051.10},
  annote =	{Keywords: Natural halting probability, natural complexity}
}

Search Results

Documents authored by Stay, Michael A.

Natural Halting Probabilities, Partial Randomness, and Zeta Functions

Abstract

Cite as

Thanks for your feedback!

Could not send message