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Original Articles

Computing a Glimpse of Randomness

, &
Pages 361-370 | Published online: 03 Apr 2012

REFERENCES

  • Bennett , C. H. and Gardner , M. 1979 . “The random number omega bids fair to hold the mysteries of the universe.” . Scientific American , 241 : 20 – 34 . [Bennett and Gardner 79]
  • Bridges , D. S. 1994 . Computability—A Mathematical Sketchbook Berlin : Springer Verlag. . [Bridges 94]
  • Calude , C. S. 1994 . Information and Randomness. An Algorithmic Perspective. Berlin : Springer-Verlag. . [Calude 94]
  • Calude , C. S. 2000 . “A glimpse into algorithmic information theory.” . In Logic, Language and Computation Edited by: Blackburn , P. , Braisby , N. , Cavedon , L. and Shimojima , A. Volume 3 , 67 – 83 . Cambridge : Cambridge University Press. . [Calude 00], CSLI Series
  • Calude , C. S. 2002 . “A characterization of c.e. random reals.” . Theoret. Comput. Sci. , 217 : 3 – 14 . [Calude 02a]
  • Calude , C. S. 2002 . “Chaitin ω numbers, Solovay machines and incompleteness.” . Theoret. Comput. Sci. , 284 : 269 – 277 . [Calude 02b]
  • Calude , C. S. and Chaitin , G. J. 1999 . “Randomness everywhere.” . Nature , 400 ( 22 ) July : 319 – 320 . [Calude and Chaitin 99]
  • Calude , C. S. , Dinneen , M. J. and Shu , C. 2000 . “Computing 80 Initial Bits of A Chaitin Omega Number: Preliminary Version.” . CDMTCS Research Report , 146 [Calude et al. 00]
  • Calude , C. S. , Hertling , P. , Khoussainov , B. and Wang , Y. “Recursively enumerable reals and Chaitin ω numbers.” . Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science . Paris . Edited by: Morvan , M. , Meinel , C. and Krob , D. pp. 596 – 606 . Berlin : Springer-Verlag. . [Calude et al. 01], Full paper in Theoret. Comput. Sci. 255 (2001), 125–149
  • Calude , C. and Jürgensen , H. 1994 . “Randomness as an invariant for number representations.” . In Results and Trends in Theoretical Computer Science Edited by: Maurer , H. , Karhumäki , J. and Rozenberg , G. 44 – 66 . Berlin : Springer-Verlag. . [Calude and Jürgensen 94]
  • Casti , J. L. 1997 . “Computing the unconfutable.” . The New Scientist , 154/2082 17 May : 34 [Casti 97]
  • Chaitin , G. J. 1975 . “A theory of program size formally identical to information theory.” . J. Assoc. Comput. Mach. , 22 : 329 – 340 . [Chaitin 75], (Reprinted in: [Chaitin 90b], 113–128)
  • Chaitin , G. J. 1987 . Algorithmic Information Theory Cambridge : Cambridge University Press. . [Chaitin 90a], (Third printing 1990)
  • Chaitin , G. J. 1987 . Information, Randomness and Incompleteness, Papers on Algorithmic Information Theory Singapore : World Scientific. . [Chaitin 90b], (2nd ed., 1990)
  • Chaitin , G. J. 1997 . The Limits of Mathematics. Singapore : Springer-Verlag. . [Chaitin 97]
  • Chaitin , G. J. 1999 . The Unknowable Singapore : Springer-Verlag. . [Chaitin 99]
  • Chaitin , G. J. 2000 . Exploring Randomness London : Springer-Verlag. . [Chaitin 00a]
  • Chaitin , G. J. November 2000 . November , [Chaitin 00b], Personal communication to C. S. Calude
  • Chaitin , G. J. December 2001 . December , [Chaitin 01], Personal communication to C. S. Calude
  • Downey , R. G. 2002 . Some Computability-Theoretical Aspects of Reals and Randomness.” . CDMTCS Research Report , 173 [Downey 02]
  • Hertling , P. and Weihrauch , K. “Randomness spaces.” . Automata, Languages and Programming, Proceedings of the 25th International Colloquium, ICALP1998 . Aalborg , Denmark. Edited by: Larsen , K. G. , Skyum , S. and Winskel , G. pp. 796 – 807 . Berlin : Springer-Verlag. . [Hertling and Weihrauch 98]
  • Kučera , A. and Slaman , T. A. 2001 . “Randomness and recursive enumerability.” . SIAM J. Comput , 31 ( 1 ) : 199 – 211 . [Kučera and Slaman 01]
  • Martin-Löf , P. 1966 . Algorithms and Random Sequences Nürnberg, Erlangen : Erlangen University. . [Martin-Löf 66]
  • Martin-Löf , P. 1966 . “The definition of random sequences.” . Inform, and Control , 9 : 602 – 619 . [Martin-Löf 66]
  • Marxen , H. and Buntrock , J. 1990 . “Attacking the busy beaver 5.” . Bull EATCS , 40 : 247 – 251 . [Marxen and Buntrock 90]
  • Odifreddi , P. 1989 . Classical Recursion Theory Vol.1 , Amsterdam : North-Holland. . [Odifreddi 99], Vol. 2, 1999
  • Shu , C. 2003 . Computing Exact Approximations of a Chaitin Omega Number , Ph.D. Thesis New Zealand : University of Auckland. . [Shu 03]
  • Soare , R. I. 1969 . “Recursion theory and Dedekind cuts.” . Trans. Amer. Math. Soc. , 140 : 271 – 294 . [Soare 69]
  • Soare , R. I. 1987 . Recursively Enumerable Sets and Degrees Berlin : Springer-Verlag. . [Soare 87]
  • Solovay , R. M. May 1975 . Draft of a paper (or series of papers) on Chaitin's work …done for the most part during the period of Sept.-Dec. 1974 May , 215 New York : IBM Thomas J. Watson Research Center, York-town Heights. . [Solovay 75], unpublished manuscript
  • Solovay , R. M. 2000 . “A version of ω for which ZFC can not predict a single bit.” . In Finite Versus Infinite. Contributions to an Eternal Dilemma Edited by: Calude , C. S. and Păun , G. 323 – 334 . London : Springer-Verlag. . [Solovay 00]
  • Staiger , L. “The Kolmogorov complexity of real numbers.” . Proc. Fundamentals of Computation Theory . Edited by: Ciobanu , G. and Păun , Gh. pp. 536 – 546 . Berlin : Springer-Verlag. . [Staiger 91], Lecture Notes in Comput. Sci. No. 1684
  • Stewart , I. 1991 . “Deciding the undecidable.” . Nature , 352 : 664 – 665 . [Stewart 91]
  • Weihrauch , K. 1987 . Computability Berlin : Springer-Verlag. . [Weihrauch 87]

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