On the existence of a new family of Diophantine equations for Ω

Fundamenta Informaticae

Volumn 56, Issue 3, 2003, Pages 273-284

  Ord, Toby ^a   Kieu, Tien D ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

; Algorithmic Information Theory; Diophantine Equation; Hilbert's Tenth Problem; Randomness

Indexed keywords

ALGORITHMS; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING; RANDOM NUMBER GENERATION;

ALGORITHMIC INFORMATION THEORY;

INFORMATION THEORY;

EID: 0242666229     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. Calude, C. S.: A Characterization of c.e. Random Reals, Theoretical Computer Science, 271, 2002, 3-14.
2. Calude, C. S., Nies, A.: Chaitin Ω Numbers and Strong Reducibilities, Journal of Universal Computer Science, 3, 1997, 1162-1166.
3. Chaitin, G. J.: A Theory of Program Size Formally Identical to Information Theory, Journal of the ACM, 22(3), July 1975, 329-340.
4. Chaitin, G. J.: Algorithmic Information Theory, Cambridge University Press, Cambridge, 1987.
5. Copeland, B. J.: Hypercomputation, Minds and Machines, 12, 2002, 461-502.
6. Copeland, B. J., Proudfoot, D.: Alan Turing's Forgotten Ideas in Computer Science, Scientific American, April 1999, 77-81.
7. Kieu, T. D.: Computing the Noncomputable, Contemporary Physics, 44, 2003, 51-71.
8. Matiyasevich, Y. Y: Hilbert's Tenth Problem, MIT Press, Cambridge, Massachusetts, 1993.
9. Ord, T.: Hypercomputation: Computing More Than the Turing Machine, Technical report, University of Melbourne, Melbourne, Australia, September 2002, Available at http://www.arxiv.org/abs/math.LO/0209332.
10. Solovay, R. M.: A Version of Ω for which ZFC Can Not Predict a Single Bit, in: Finite Versus Infinite. Contributions to an Eternal Dilemma (C. S. Calude, G. Pǎun, Eds.), Springer, London, 2000, 323-334.