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Volumn 11, Issue 3, 2002, Pages 361-370

Computing a glimpse of randomness

Author keywords

Algorithmic randomness; Chaitin Omega number; Halting problem

Indexed keywords


EID: 0036942286     PISSN: 10586458     EISSN: None     Source Type: Journal    
DOI: 10.1080/10586458.2002.10504481     Document Type: Article
Times cited : (34)

References (35)
  • 1
    • 0009228180 scopus 로고
    • The random number omega bids fair to hold the mysteries of the universe
    • [Bennett and Gardner 79]
    • [Bennett and Gardner 79] C. H. Bennett, M. Gardner. "The random number omega bids fair to hold the mysteries of the universe." Scientific American 241 (1979), 20-34.
    • (1979) Scientific American , vol.241 , pp. 20-34
    • Bennett, C.H.1    Gardner, M.2
  • 4
    • 0012383185 scopus 로고    scopus 로고
    • A glimpse into algorithmic information theory
    • [Calude 00] in Logic, Language and Computation, P. Blackburn, N. Braisby, L. Cavedon, A. Shimojima (eds.), Cambridge University Press, Cambridge
    • [Calude 00] C. S. Calude. "A glimpse into algorithmic information theory." in Logic, Language and Computation, P. Blackburn, N. Braisby, L. Cavedon, A. Shimojima (eds.), Volume 3, CSLI Series, pp. 67-83, Cambridge University Press, Cambridge, 2000.
    • (2000) CSLI Series , vol.3 , pp. 67-83
    • Calude, C.S.1
  • 5
    • 0037185197 scopus 로고    scopus 로고
    • A characterization of c.e. random reals
    • [Calude 02a]
    • [Calude 02a] C. S. Calude. "A characterization of c.e. random reals." Theoret. Comput. Sci., 217 (2002), 3-14.
    • (2002) Theoret. Comput. Sci. , vol.217 , pp. 3-14
    • Calude, C.S.1
  • 6
    • 0037189793 scopus 로고    scopus 로고
    • Chaitin Ω numbers, Solovay machines and incompleteness
    • [Calude 02b]
    • [Calude 02b] C. S. Calude. "Chaitin Ω numbers, Solovay machines and incompleteness." Theoret. Comput. Sci. 284 (2002), 269-277.
    • (2002) Theoret. Comput. Sci. , vol.284 , pp. 269-277
    • Calude, C.S.1
  • 7
    • 0033595272 scopus 로고    scopus 로고
    • Randomness everywhere
    • [Calude and Chaitin 99] July
    • [Calude and Chaitin 99] C. S. Calude and G. J. Chaitin. "Randomness everywhere." Nature, 400:22 (July 1999), 319-320.
    • (1999) Nature , vol.400 , Issue.22 , pp. 319-320
    • Calude, C.S.1    Chaitin, G.J.2
  • 8
    • 0012382081 scopus 로고    scopus 로고
    • Computing 80 initial bits of A Chaitin Omega number: Preliminary version
    • [Calude et al. 00]
    • [Calude et al. 00] C. S. Calude, M. J. Dinneen, and C. Shu. "Computing 80 Initial Bits of A Chaitin Omega Number: Preliminary Version." CDMTCS Research Report 146 (2000)
    • (2000) CDMTCS Research Report , vol.146
    • Calude, C.S.1    Dinneen, M.J.2    Shu, C.3
  • 9
    • 78649893518 scopus 로고    scopus 로고
    • Recursively enumerable reals and Chaitin Ω numbers
    • [Calude et al. 01] M. Morvan, C. Meinel, D. Krob (eds.), Springer-Verlag, Berlin
    • [Calude et al. 01] C. S. Calude, P. Hertling, B. Khoussainov, and Y. Wang. "Recursively enumerable reals and Chaitin Ω numbers." in Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science (Paris), M. Morvan, C. Meinel, D. Krob (eds.), pp. 596-606, Springer-Verlag, Berlin, 1998. Full paper in Theoret. Comput. Sci. 255 (2001), 125-149.
    • (1998) Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science (Paris) , pp. 596-606
    • Calude, C.S.1    Hertling, P.2    Khoussainov, B.3    Wang, Y.4
  • 10
    • 0034899598 scopus 로고    scopus 로고
    • [Calude et al. 01] C. S. Calude, P. Hertling, B. Khoussainov, and Y. Wang. "Recursively enumerable reals and Chaitin Ω numbers." in Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science (Paris), M. Morvan, C. Meinel, D. Krob (eds.), pp. 596-606, Springer-Verlag, Berlin, 1998. Full paper in Theoret. Comput. Sci. 255 (2001), 125-149.
    • (2001) Theoret. Comput. Sci. , vol.255 , pp. 125-149
  • 11
    • 0002429893 scopus 로고
    • Randomness as an invariant for number representations
    • [Calude and Jürgensen 94] H. Maurer, J. Karhumäki, G. Rozenberg (eds.), Springer-Verlag, Berlin
    • [Calude and Jürgensen 94] C. Calude and H. Jürgensen. "Randomness as an invariant for number representations." in Results and Trends in Theoretical Computer Science, H. Maurer, J. Karhumäki, G. Rozenberg (eds.), pp. 44-66, Springer-Verlag, Berlin, 1994.
    • (1994) Results and Trends in Theoretical Computer Science , pp. 44-66
    • Calude, C.1    Jürgensen, H.2
  • 12
    • 0002421797 scopus 로고    scopus 로고
    • Computing the uncomputable
    • [Casti 97] 17 May
    • [Casti 97] J. L. Casti. "Computing the uncomputable." The New Scientist, 154/2082 (17 May 1997), 34.
    • (1997) The New Scientist , vol.154 , Issue.2082 , pp. 34
    • Casti, J.L.1
  • 13
    • 0016532771 scopus 로고
    • A theory of program size formally identical to information theory
    • [Chaitin 75] (Reprinted in: [Chaitin 90b], 113-128)
    • [Chaitin 75] G. J. Chaitin. "A theory of program size formally identical to information theory." J. Assoc. Comput. Mach. 22 (1975), 329-340. (Reprinted in: [Chaitin 90b], 113-128)
    • (1975) J. Assoc. Comput. Mach. , vol.22 , pp. 329-340
    • Chaitin, G.J.1
  • 14
    • 0003781308 scopus 로고
    • [Chaitin 90a] Cambridge University Press, Cambridge, (Third printing 1990)
    • [Chaitin 90a] G. J. Chaitin. Algorithmic Information Theory, Cambridge University Press, Cambridge, 1987. (Third printing 1990)
    • (1987) Algorithmic Information Theory
    • Chaitin, G.J.1
  • 17
    • 0003602295 scopus 로고    scopus 로고
    • [Chaitin 99] Springer-Verlag, Singapore
    • [Chaitin 99] G. J. Chaitin. The Unknowable, Springer-Verlag, Singapore, 1999.
    • (1999) The Unknowable
    • Chaitin, G.J.1
  • 18
    • 0003497245 scopus 로고    scopus 로고
    • [Chaitin 00a] Springer-Verlag, London
    • [Chaitin 00a] G. J. Chaitin. Exploring Randomness, Springer-Verlag, London, 2000.
    • (2000) Exploring Randomness
    • Chaitin, G.J.1
  • 19
    • 85021009018 scopus 로고    scopus 로고
    • [Chaitin 00b] Personal communication to C. S. Calude, November
    • [Chaitin 00b] G. J. Chaitin. Personal communication to C. S. Calude, November 2000.
    • (2000)
    • Chaitin, G.J.1
  • 20
    • 85020990802 scopus 로고    scopus 로고
    • [Chaitin 01] Personal communication to C. S. Calude, December
    • [Chaitin 01] G. J. Chaitin. Personal communication to C. S. Calude, December 2001.
    • (2001)
    • Chaitin, G.J.1
  • 21
    • 0012386365 scopus 로고    scopus 로고
    • Some computability-theoretical aspects of reals and randomness
    • [Downey 02]
    • [Downey 02] R. G. "Downey. Some Computability-Theoretical Aspects of Reals and Randomness." CDMTCS Research Report 173 (2002).
    • (2002) CDMTCS Research Report , vol.173
    • Downey, R.G.1
  • 23
    • 0036214633 scopus 로고    scopus 로고
    • Randomness and recursive enumerability
    • [Kučera and Slaman 01]
    • [Kučera and Slaman 01] A. Kucera and T. A. Slaman. "Randomness and recursive enumerability." SIAM J. Comput., 31:1 (2001), 199-211.
    • (2001) SIAM J. Comput. , vol.31 , Issue.1 , pp. 199-211
    • Kucera, A.1    Slaman, T.A.2
  • 24
    • 0004216089 scopus 로고
    • [Martin-Löf 66] Erlangen University, Nürnberg, Erlangen
    • [Martin-Löf 66] P. Martin-Löf. Algorithms and Random Sequences, Erlangen University, Nürnberg, Erlangen, 1966.
    • (1966) Algorithms and Random Sequences
    • Martin-Löf, P.1
  • 25
    • 18344371384 scopus 로고
    • The definition of random sequences
    • [Martin-Löf 66]
    • [Martin-Löf 66] P. Martin-Löf. "The definition of random sequences." Inform. and Control 9 (1966), 602-619.
    • (1966) Inform. and Control , vol.9 , pp. 602-619
    • Martin-Löf, P.1
  • 26
    • 0001150418 scopus 로고
    • Attacking the busy beaver 5
    • [Marxen and Buntrock 90]
    • [Marxen and Buntrock 90] H. Marxen and J. Buntrock. "Attacking the busy beaver 5." Bull EATCS 40 (1990), 247-251.
    • (1990) Bull EATCS , vol.40 , pp. 247-251
    • Marxen, H.1    Buntrock, J.2
  • 27
    • 85021021488 scopus 로고
    • [Odifreddi 99] North-Holland, Amsterdam
    • [Odifreddi 99] P. Odifreddi. Classical Recursion Theory, North-Holland, Amsterdam, Vol.1, 1989, Vol. 2, 1999.
    • (1989) Classical Recursion Theory , vol.1-2
    • Odifreddi, P.1
  • 29
    • 0000645113 scopus 로고
    • Recursion theory and Dedekind cuts
    • [Scare 69]
    • [Scare 69] R. I. Scare. "Recursion theory and Dedekind cuts." Trans. Amer. Math. Soc. 140 (1969), 271-294.
    • (1969) Trans. Amer. Math. Soc. , vol.140 , pp. 271-294
    • Scare, R.I.1
  • 32
    • 0002281062 scopus 로고    scopus 로고
    • A version of Ω for which ZFC can not predict a single bit
    • [Solovay 00] C.S. Calude, G. Pǎun (eds.), Springer-Verlag, London
    • [Solovay 00] R. M. Solovay. "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.), pp. 323-334, Springer-Verlag, London, 2000.
    • (2000) Finite Versus Infinite. Contributions to an Eternal Dilemma , pp. 323-334
    • Solovay, R.M.1
  • 33
    • 84956855154 scopus 로고    scopus 로고
    • The Kolmogorov complexity of real numbers
    • [Staiger 91] in Proc. Fundamentals of Computation Theory, G. Ciobanu and Gh. Pǎun (eds.), Springer-Verlag, Berlin
    • [Staiger 91] L. Staiger. "The Kolmogorov complexity of real numbers." in Proc. Fundamentals of Computation Theory, Lecture Notes in Comput. Sci. No. 1684, G. Ciobanu and Gh. Pǎun (eds.), pp. 536-546, Springer-Verlag, Berlin, 1999.
    • (1999) Lecture Notes in Comput. Sci. , vol.1684 , pp. 536-546
    • Staiger, L.1
  • 34
    • 0001708005 scopus 로고
    • Deciding the undecidable
    • [Stewart 91]
    • [Stewart 91] I. Stewart. "Deciding the undecidable." Nature 352 (1991), 664-665.
    • (1991) Nature , vol.352 , pp. 664-665
    • Stewart, I.1
  • 35
    • 0003466692 scopus 로고
    • [Weihrauch 87] Springer-Verlag, Berlin
    • [Weihrauch 87] K. Weihrauch. Computability, Springer-Verlag, Berlin, 1987.
    • (1987) Computability
    • Weihrauch, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.