Prediction and dimension

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 2375, Issue , 2002, Pages 380-395

  Fortnow, Lance ^a   Lutz, Jack H ^b  

^a NEC LABORATORIES AMERICA   (United States)

^b Iowa State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; POLYNOMIAL APPROXIMATION; POLYNOMIALS;

FEASIBLE DIMENSION; FINITE ALPHABET; HAUSDORFF DIMENSION; POLYNOMIAL-TIME; SELF INFORMATION; SUCCESS RATIO;

FRACTAL DIMENSION;

EID: 84937416143     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/3-540-45435-7_26     Document Type: Conference Paper

References (25)

1. J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I (second edition). Springer-Verlag, Berlin, 1995.
2. N. Cesa-Bianchi, Y. Freund, D. Haussler, D. P. Helmbold, R. E. Schapire, and M. K. Warmuth. Howto use expert advice. Journal of the ACM, 44(3):427-485, May 1997.
3. N. Cesa-Bianchi and G. Lugosi. On prediction of individual sequences. Annals of Statistics, 27(6):1865-1895, 1999.
4. T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley & Sons, Inc., New York, N.Y., 1991.
5. J. J. Dai, J. I. Lathrop, J. H. Lutz, and E. Mayordomo. Finite-state dimension. In Proceedings of the Twenty-Eighth International Colloquium on Automata, Languages, and Programming, pages 1028-1039. Springer-Verlag, 2001.
6. K. Falconer. Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, 1990.
7. M. Feder. Gambling using a finite state machine. IEEE Transactions on Information Theory, 37:1459-1461, 1991.
8. M. Feder, N. Merhav, and M. Gutman. Universal prediction of individual sequences. IEEE Transations on Information Theory, 38:1258-1270, 1992.
9. F. Hausdorff. Dimension und äusseres Mass. Math. Ann., 79:157-179, 1919.
10. J. Kelly. A newin terpretation of information rate. Bell Systems Technical Journal, 35:917-926, 1956.
11. A. N. Kolmogorov. On tables of random numbers. Sankhya¯, Series A, 25:369-376, 1963.
12. D. W. Loveland. A newin terpretation of von Mises' concept of a random sequence. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 12:279-294, 1966.
13. J. H. Lutz. Dimension in complexity classes. In Proceedings of the Fifteenth Annual IEEE Conference on Computational Complexity, pages 158-169. IEEE Computer Society Press, 2000. Updated version appears as Technical report cs.CC/0203016, ACM Computing Research Repository, 2002.
14. J. H. Lutz. Gales and the constructive dimension of individual sequences. In Proceedings of the Twenty-Seventh International Colloquium on Automata, Languages, and Programming, pages 902-913. Springer-Verlag, 2000. Updated version appears as Technical report cs.CC/0203017, ACM Computing Research Repository, 2002.
15. D. A. Martin. Classes of recursively enumerable sets and degrees of unsolvability. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 12:295-310, 1966.
16. B. Ya. Ryabko. Noiseless coding of combinatorial sources. Problems of Information Transmission, 22:170-179, 1986.
17. B. Ya. Ryabko. Algorithmic approach to the prediction problem. Problems of Information Transmission, 29:186-193, 1993.
18. B. Ya. Ryabko. The complexity and effectiveness of prediction problems. Journal of Complexity, 10:281-295, 1994.
19. C. P. Schnorr. A unified approach to the definition of random sequences. Mathematical Systems Theory, 5:246-258, 1971.
20. C. P. Schnorr. Zufälligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics, 218, 1971.
21. C. E. Shannon. Certain results in coding theory for noisy channels. Bell Systems Technical Journal, 30:50-64, 1951.
22. A. Kh. Sheń. On relations between different algorithmic definitions of randomness. Soviet Mathematics Doklady, 38:316-319, 1989.
23. L. Staiger. Kolmogorov complexity and Hausdorff dimension. Information and Control, 103:159-94, 1993.
24. L. Staiger. A tight upper bound on Kolmogorov complexity and uniformly optimal prediction. Theory of Computing Systems, 31:215-29, 1998.
25. V. Vovk. A game of prediction with expert advice. Journal of Computer and System Sciences, pages 153-173, 1998.