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Volumn 93, Issue 3, 2005, Pages 149-153

Constructive dimension equals Kolmogorov complexity

Author keywords

Constructive dimension; Kolmogorov complexity; Levin's universal semi measure; Theory of computation

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; FRACTALS; SET THEORY; THEOREM PROVING;

EID: 10444249657     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2004.09.023     Document Type: Article
Times cited : (25)

References (20)
  • 2
    • 0028712369 scopus 로고
    • On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line
    • J. Cai, J. Hartmanis, On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line, J. Comput. Systems Sci. 49 (1994) 605-619.
    • (1994) J. Comput. Systems Sci. , vol.49 , pp. 605-619
    • Cai, J.1    Hartmanis, J.2
  • 5
    • 0037447594 scopus 로고    scopus 로고
    • Gales suffice for constructive dimension
    • J.M. Hitchcock, Gales suffice for constructive dimension, Inform. Process. Lett. 86 (2003) 9-12.
    • (2003) Inform. Process. Lett. , vol.86 , pp. 9-12
    • Hitchcock, J.M.1
  • 7
    • 0345227319 scopus 로고    scopus 로고
    • Dimension in complexity classes
    • J.H. Lutz, Dimension in complexity classes, SIAM J. Comput. 32 (2003) 1236-1250.
    • (2003) SIAM J. Comput. , vol.32 , pp. 1236-1250
    • Lutz, J.H.1
  • 9
    • 0344118726 scopus 로고    scopus 로고
    • The dimensions of individual strings and sequences
    • J.H. Lutz, The dimensions of individual strings and sequences, Inform, and Comput. 187 (2003) 49-79.
    • (2003) Inform. Comput. , vol.187 , pp. 49-79
    • Lutz, J.H.1
  • 10
    • 0037120704 scopus 로고    scopus 로고
    • A Kolmogorov complexity characterization of constructive Hausdorff dimension
    • E. Mayordomo, A Kolmogorov complexity characterization of constructive Hausdorff dimension, Inform. Process. Lett. 84 (2002) 1-3.
    • (2002) Inform. Process. Lett. , vol.84 , pp. 1-3
    • Mayordomo, E.1
  • 12
    • 0004492226 scopus 로고
    • Coding of combinatorial sources and Hausdorff dimension
    • B.Ya. Ryabko, Coding of combinatorial sources and Hausdorff dimension, Soviet Math. Dokl. 30 (1) (1984) 219-222.
    • (1984) Soviet Math. Dokl. , vol.30 , Issue.1 , pp. 219-222
    • Ryabko, B.Ya.1
  • 13
    • 0022741249 scopus 로고
    • Noiseless coding of combinatorial sources
    • B.Ya. Ryabko, Noiseless coding of combinatorial sources, Probl. Inform. Transmission 22 (1986) 170-179.
    • (1986) Probl. Inform. Transmission , vol.22 , pp. 170-179
    • Ryabko, B.Ya.1
  • 14
    • 0000797906 scopus 로고
    • The complexity and effectiveness of prediction problems
    • B.Ya. Ryabko, The complexity and effectiveness of prediction problems, J. Complexity 10 (1994) 281-295.
    • (1994) J. Complexity , vol.10 , pp. 281-295
    • Ryabko, B.Ya.1
  • 15
    • 38249002230 scopus 로고
    • Kolmogorov complexity and Hausdorff dimension
    • L. Staiger, Kolmogorov complexity and Hausdorff dimension, Inform, and Comput. 103 (1993) 159-194.
    • (1993) Inform. and Comput. , vol.103 , pp. 159-194
    • Staiger, L.1
  • 16
    • 0038856793 scopus 로고    scopus 로고
    • A tight upper bound on Kolmogorov complexity and uniformly optimal prediction
    • L. Staiger, A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 (1998) 215-229.
    • (1998) Theory Comput. Syst. , vol.31 , pp. 215-229
    • Staiger, L.1
  • 17
    • 0037189796 scopus 로고    scopus 로고
    • The Kolmogorov complexity of real numbers
    • L. Staiger, The Kolmogorov complexity of real numbers, Theoret. Comput. Sci. 284 (2002) 455-466.
    • (2002) Theoret. Comput. Sci. , vol.284 , pp. 455-466
    • Staiger, L.1
  • 18
    • 10444239935 scopus 로고    scopus 로고
    • A generalization of Chaitin's halting probability Ω and halting self-similar sets
    • K. Tadaki, A generalization of Chaitin's halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 (2002) 219-253.
    • (2002) Hokkaido Math. J. , vol.31 , pp. 219-253
    • Tadaki, K.1
  • 19
    • 8744282544 scopus 로고    scopus 로고
    • Relations between varieties of Kolmogorov complexities
    • V.A. Uspensky, A. Shen, Relations between varieties of Kolmogorov complexities, Math. Systems Theory 29 (1996) 271-292.
    • (1996) Math. Systems Theory , vol.29 , pp. 271-292
    • Uspensky, V.A.1    Shen, A.2
  • 20
    • 77951203397 scopus 로고
    • Complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms
    • A.K. Zvonkin, L.A. Levin, Complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms, Russian Math. Surv. 25 (1970) 83-124.
    • (1970) Russian Math. Surv. , vol.25 , pp. 83-124
    • Zvonkin, A.K.1    Levin, L.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.