How (not) to Compute the Halting Probability-Reference-Cited by-同舟云学术

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How (not) to Compute the Halting Probability

Published:2024-04-05 Issue: Volume: Page:
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Author:

Jalilvand Manizheh,Nikzad Behzad,Salehi Saeed^ORCID

Abstract

We study Chaitin’s well-known constant number Omega, and show that it is not a probability of halting the randomly chosen input-free programs. We suggest some methods for defining the halting probabilities by various measures.

Publisher

Qeios Ltd

Link

https://www.qeios.com/read/FTEFK8/pdf

Reference20 articles.

1. Glazier, Harriet E. (1916); The Mathematics of Common Things, School Science and Mathematics 16:8, pp. 667–674. doi: 10.1111/j.1949-8594.1916.tb01753.x

2. Linde, Werner (2024); Probability Theory: A First Course in Probability Theory and Statistics, De Gruyter (2nd ed.). isbn: 9783111324845

3. Chaitin, Gregory J. (1975); A Theory of Program Size Formally Identical to Information Theory, Journal of the Association for Computing Machinery 22:3, pp. 329–340. doi: 10.1145/321892.321894

4. Chaitin, Gregory J. (1988); Randomness in Arithmetic, Scientific American 259:1 (July), pp. 80–85. Jstor: 24989161

5. Rozenberg, Grzegorz & Salomaa, Arto (2007); “The Secret Number: An Exposition of Chaitin’s Theory”, in: C. S. Calude (ed.), Randomness and Complexity: From Leibniz to Chaitin, World Scientific, pp. 175–215. doi: 10.1142/9789812770837_0011

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