Notre Dame Journal of Formal Logic

The Halting Problem Is Decidable on a Set of Asymptotic Probability One

Joel David Hamkins and Alexei Miasnikov

Abstract

The halting problem for Turing machines is decidable on a set of asymptotic probability one. The proof is sensitive to the particular computational models.

Article information

Source
Notre Dame J. Formal Logic Volume 47, Number 4 (2006), 515-524.

Dates
First available in Project Euclid: 9 January 2007

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1168352664

Digital Object Identifier
doi:10.1305/ndjfl/1168352664

Mathematical Reviews number (MathSciNet)
MR2272085

Zentralblatt MATH identifier
1137.03024

Subjects
Primary: 03D10: Turing machines and related notions [See also 68Q05]
Secondary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]

Keywords
Turing machines halting problem decidability

Citation

Hamkins, Joel David; Miasnikov, Alexei. The Halting Problem Is Decidable on a Set of Asymptotic Probability One. Notre Dame J. Formal Logic 47 (2006), no. 4, 515--524. doi:10.1305/ndjfl/1168352664. http://projecteuclid.org/euclid.ndjfl/1168352664.


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References

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  • [3] Soare, R. I., Recursively Enumerable Sets and Degrees. A Study of Computable Functions and Computably Generated Sets, Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1987.