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Computer Science > Information Theory

arXiv:0804.3459 (cs)
[Submitted on 22 Apr 2008 (v1), last revised 1 Jun 2010 (this version, v3)]

Title:Towards a stable definition of Kolmogorov-Chaitin complexity

Authors:Jean-Paul Delahaye, Hector Zenil
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Abstract:Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the Kolmogorov-Chaitin complexity of a string s. Some attempts have been made to arrive at a framework stable enough for a concrete definition of K, independent of any constant under a programming language, by appealing to the "naturalness" of the language in question. The aim of this paper is to present an approach to overcome the problem by looking at a set of models of computation converging in output probability distribution such that that "naturalness" can be inferred, thereby providing a framework for a stable definition of K under the set of convergent models of computation.
Comments: 15 pages, 4 figures, 2 tables. V2 minor typo corrections. Paper web page on Experimental Algorithmic Information Theory: http://http://www.this http URL
Subjects: Information Theory (cs.IT); Computational Complexity (cs.CC)
Cite as: arXiv:0804.3459 [cs.IT]
  (or arXiv:0804.3459v3 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.0804.3459

Submission history

From: Hector Zenil [view email]
[v1] Tue, 22 Apr 2008 07:18:37 UTC (181 KB)
[v2] Mon, 5 May 2008 04:30:38 UTC (181 KB)
[v3] Tue, 1 Jun 2010 20:04:14 UTC (181 KB)
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