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Volumn 13, Issue 4, 2002, Pages 587-612

Hierarchies of generalized kolmogorov complexities and nonenumerable universal measures computable in the limit

Author keywords

computability in the limit; computable universes; cumulatively enumerable measures; generalized algorithmic probability; generalized Kolmogorov complexity hierarchy; halting probability Omega

Indexed keywords


EID: 1642358077     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129054102001291     Document Type: Article
Times cited : (64)

References (45)
  • 1
    • 84889516607 scopus 로고
    • Algorithmic information theory
    • Reidel, Kluwer Academic Publishers
    • Y. M. Barzdin. Algorithmic information theory. In Encyclopaedia of Mathematics, volume 1, pages 140-142. Reidel, Kluwer Academic Publishers, 1988.
    • (1988) Encyclopaedia of Mathematics, Volume 1 , pp. 140-142
    • Barzdin, Y.M.1
  • 3
    • 0034673710 scopus 로고    scopus 로고
    • Quantum information and computation
    • C. H. Bennett and D. P. DiVicenzo. Quantum information and computation. Nature, 404(6775):256-259, 2000.
    • (2000) Nature , vol.404 , Issue.6775 , pp. 256-259
    • Bennett, C.H.1    Divicenzo, D.P.2
  • 7
    • 28344432388 scopus 로고    scopus 로고
    • Theory of super-recursive algorithms as a source of a new paradigm for computer simulation
    • Washington
    • M. S. Burgin. Theory of super-recursive algorithms as a source of a new paradigm for computer simulation. In Proceedings of the Business and Industry Simulation Symposium, pages 70-75. Washington, 2000.
    • (2000) Proceedings of the Business and Industry Simulation Symposium , pp. 70-75
    • Burgin, M.S.1
  • 9
    • 84967357698 scopus 로고    scopus 로고
    • Chaitin O numbers, Solovay machines and Godel incompleteness
    • In press
    • C. S. Calude. Chaitin O numbers, Solovay machines and Godel incompleteness. Theoretical Computer Science, 2001. In press.
    • (2001) Theoretical Computer Science
    • Calude, C.S.1
  • 11
    • 78649699122 scopus 로고
    • Uber eine eigenschaft des inbegriftes aller reellen algebraischen zahlen
    • G. Cantor. Uber eine Eigenschaft des InbegrifTes aller reellen algebraischen Zahlen. Crelle's Journal fur Mathematik, 77:258-263, 1874.
    • (1874) Crelle's Journal fur Mathematik , vol.77 , pp. 258-263
    • Cantor, G.1
  • 13
    • 77954563357 scopus 로고
    • On the length of programs for computing finite binary sequences: Statistical considerations
    • Submitted 1965
    • G.J. Chaitin. On the length of programs for computing finite binary sequences: statistical considerations. Journal of the ACM, 16:145-159, 1969. Submitted 1965.
    • (1969) Journal of the ACM , vol.16 , pp. 145-159
    • Chaitin, G.J.1
  • 16
    • 0000189643 scopus 로고
    • On the symmetry of algorithmic information
    • P. Gacs. On the symmetry of algorithmic information. Soviet Math. Dokl., 15:1477-1480, 1974.
    • (1974) Soviet Math. Dokl. , vol.15 , pp. 1477-1480
    • Gacs, P.1
  • 17
    • 0006892523 scopus 로고
    • On the relation between descriptional complexity and algorithmic probability
    • P. Gacs. On the relation between descriptional complexity and algorithmic probability. Theoretical Computer Science, 22:71-93, 1983.
    • (1983) Theoretical Computer Science , vol.22 , pp. 71-93
    • Gacs, P.1
  • 18
    • 34347193348 scopus 로고
    • Uber formal unentscheidbare satze der principia mathematica und verwandter systeme i
    • K. Godel. Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I. Monatshefte fur Mathematik und Physik, 38:173-198, 1931.
    • (1931) Monatshefte fur Mathematik und Physik , vol.38 , pp. 173-198
    • Godel, K.1
  • 19
    • 0002295357 scopus 로고
    • Limiting recursion
    • E. M. Gold. Limiting recursion. Journal of Symbolic Logic, 30(l):28-46, 1965.
    • (1965) Journal of Symbolic Logic , vol.30 , Issue.1 , pp. 28-46
    • Gold, E.M.1
  • 20
    • 0002113398 scopus 로고
    • On the definitions of computable real continuous functions
    • A. Gregorczyk. On the definitions of computable real continuous functions. Fundamenta Mathematicae, 44:61-71, 1957.
    • (1957) Fundamenta Mathematicae , vol.44 , pp. 61-71
    • Gregorczyk, A.1
  • 22
    • 84938015047 scopus 로고
    • A method for construction of minimum-redundancy codes
    • D. A. Huffman. A method for construction of minimum-redundancy codes. Proceedings IRE, 40:1098-1101, 1952.
    • (1952) Proceedings IRE , vol.40 , pp. 1098-1101
    • Huffman, D.A.1
  • 23
    • 0043054819 scopus 로고    scopus 로고
    • General loss bounds for universal sequence prediction
    • Springer 2001. TR IDSIA-03-01, IDSIA, Switzerland, Jan, cs.AI/0101019
    • M. Hutter. General loss bounds for universal sequence prediction. In Proceedings of the 18t/l International Conference on Machine Learning (ICML-2001). Springer, 2001. TR IDSIA-03-01, IDSIA, Switzerland, Jan 2001, cs.AI/0101019.
    • (2001) Proceedings of the 18t/l International Conference on Machine Learning (ICML-2001)
    • Hutter, M.1
  • 24
    • 0035360790 scopus 로고    scopus 로고
    • New error bounds for Solomonoff prediction
    • M. Hutter. New error bounds for Solomonoff prediction. Journal of Computer and System Science, 62(4):653-667, 2001. http://xxx.lanl.gov/abs/cs.AI/ 9912008.
    • (2001) Journal of Computer and System Science , vol.62 , Issue.4 , pp. 653-667
    • Hutter, M.1
  • 25
    • 0001902056 scopus 로고
    • Three approaches to the quantitative definition of information
    • A.N. Kolmogorov. Three approaches to the quantitative definition of information. Problems of Information Transmission, 1:1-11, 1965.
    • (1965) Problems of Information Transmission , vol.1 , pp. 1-11
    • Kolmogorov, A.N.1
  • 26
    • 38249002629 scopus 로고
    • On relative randomness
    • A. Kucera. On relative randomness. Ann. Pure Appl. Logic, 63(l):61-67, 1993.
    • (1993) Ann. Pure Appl. Logic , vol.63 , Issue.1 , pp. 61-67
    • Kucera, A.1
  • 27
    • 0020733207 scopus 로고
    • On the random oracle hypothesis
    • S. A. Kurtz. On the random oracle hypothesis. Inform, and Control, 57:40-47, 1983.
    • (1983) Inform, and Control , vol.57 , pp. 40-47
    • Kurtz, S.A.1
  • 28
    • 0000508181 scopus 로고
    • On the notion of a random sequence
    • L. A. Levin. On the notion of a random sequence. Soviet Math. Dokl., 14(5):1413-1416, 1973.
    • (1973) Soviet Math. Dokl. , vol.14 , Issue.5 , pp. 1413-1416
    • Levin, L.A.1
  • 29
    • 0016078993 scopus 로고
    • Laws of information (nongrowth) and aspects of the foundation of probability theory
    • L. A. Levin. Laws of information (nongrowth) and aspects of the foundation of probability theory. Problems of Information Transmission, 10(3):206-210, 1974.
    • (1974) Problems of Information Transmission , vol.10 , Issue.3 , pp. 206-210
    • Levin, L.A.1
  • 31
    • 18344371384 scopus 로고
    • L6f the definition of random sequences
    • P. Martin-L6f. The definition of random sequences. Information and Control, 9:602-619, 1966.
    • (1966) Information and Control , vol.9 , pp. 602-619
    • Martin, P.1
  • 33
    • 0002019785 scopus 로고
    • Trial and error predicates and the solution to a problem of Mostowski
    • H. Putnam. Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic, 30(l):49-57, 1965.
    • (1965) Journal of Symbolic Logic , vol.30 , Issue.1 , pp. 49-57
    • Putnam, H.1
  • 35
    • 0041644968 scopus 로고    scopus 로고
    • A computer scientist's view of life, the universe, and everything
    • In C. Preksa, M. Jantzen, and R. Valk, editors. Lecture Notes in Computer Science, Springer, Berlin,. Submitted 1996.
    • J. Schmidhuber. A computer scientist's view of life, the universe, and everything. In C. Preksa, M. Jantzen, and R. Valk, editors, Foundations of Computer Science: Potential-Theory-Cognition, volume 1337, pages 201-208. Lecture Notes in Computer Science, Springer, Berlin, 1997. Submitted 1996.
    • (1997) Foundations of Computer Science: Potential-Theory-Cognition , vol.1337 , pp. 201-208
    • Schmidhuber, J.1
  • 36
    • 1642374463 scopus 로고    scopus 로고
    • Technical Report IDSIA-20-00, quant-ph/0011122, IDSIA, Manno (Lugano), Switzerland
    • J. Schmidhuber. Algorithmic theories of everything. Technical Report IDSIA-20-00, quant-ph/0011122, IDSIA, Manno (Lugano), Switzerland, 2000.
    • (2000) Algorithmic Theories of Everything
    • Schmidhuber, J.1
  • 37
    • 0015902552 scopus 로고
    • Process complexity and effective random tests
    • C. P. Schnorr. Process complexity and effective random tests. Journal of Computer Systems Science, 7:376-388, 1973.
    • (1973) Journal of Computer Systems Science , vol.7 , pp. 376-388
    • Schnorr, C.P.1
  • 38
    • 84940644968 scopus 로고
    • A mathematical theory of communication (parts i and II)
    • C. E. Shannon. A mathematical theory of communication (parts I and II). Bell System Technical Journal, XXVII:379-423, 1948.
    • (1948) Bell System Technical Journal , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 39
    • 4243694246 scopus 로고    scopus 로고
    • Technical report Univ. of California, Berkeley
    • T. Slaman. Randomness and recursive enumerability. Technical report, Univ. of California, Berkeley, 1999. Preprint, http://www.math.berkeley.edu/ ~slaman.
    • (1999) Randomness and Recursive Enumerability
    • Slaman, T.1
  • 42
    • 0002281062 scopus 로고    scopus 로고
    • A version of O for which ZFC can not predict a single bit
    • In C. S. Calude and G. Paun, editors. Springer, London,.
    • R. M. Solovay. A version of O for which ZFC can not predict a single bit. In C. S. Calude and G. Paun, editors, Finite Versus Infinite. Contributions to an Eternal Dilemma, pages 323-334. Springer, London, 2000.
    • (2000) Finite Versus Infinite. Contributions to An Eternal Dilemma , pp. 323-334
    • Solovay, R.M.1
  • 43
    • 84960561455 scopus 로고
    • On computable numbers, with an application to the Entscheidungsproblem
    • A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Series 2, 41:230-267, 1936.
    • (1936) Proceedings of the London Mathematical Society, Series , vol.2 , Issue.41 , pp. 230-267
    • Turing, A.M.1
  • 44
    • 0013361657 scopus 로고    scopus 로고
    • Non-stochastic infinite and finite sequences
    • V. V. V'yugin. Non-stochastic infinite and finite sequences. Theoretical Computer Science, 207(2):363-382, 1998.
    • (1998) Theoretical Computer Science , vol.207 , Issue.2 , pp. 363-382
    • V'Yugin, V.V.1
  • 45
    • 77951203397 scopus 로고
    • The complexity of finite objects and the algorithmic concepts of information and randomness
    • A. K. Zvonkin and L. A. Levin. The complexity of finite objects and the algorithmic concepts of information and randomness. Russian Math. Surveys, 25(6).-83-124, 1970.
    • (1970) Russian Math. Surveys , vol.25 , Issue.6 , pp. 83-124
    • Zvonkin, A.K.1    Levin, L.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.