Download This PaperHow (not) to Compute the Halting Probability
2020 Math Subject Classification: 60A10 · 28A05 · 68Q04 · 03D10.
12 Pages Posted: 29 Dec 2023 Last revised: 2 Jan 2024
Date Written: June 15, 2024
Abstract
We study Chaitin's well-known constant Omega, and show that this number is not a probability of halting the randomly chosen input-free programs under any infinite discrete measure. We suggest some methods for defining the halting probabilities by various measures.
Keywords: Chaitin's Constant, The Omega Number, Halting Probability, Probability Measure, Kolmogorov Axioms, Random Numbers, Algorithmic Information Theory. 2020 Math Subject Classification: 60A10, 28A05, 68Q04, 03D10
Suggested Citation: Suggested Citation
Jalilvand, Manizheh and Nikzad, Behzad and Salehi, Saeed, How (not) to Compute the Halting Probability (June 15, 2024). 2020 Math Subject Classification: 60A10 · 28A05 · 68Q04 · 03D10., Available at SSRN: https://ssrn.com/abstract=4602807 or http://dx.doi.org/10.2139/ssrn.4602807
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