Dimension, entropy rates, and compression

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn 19, Issue , 2004, Pages 174-183

  Hitchcock, John M ^a   Vinodchandran, N V ^b  

^a UNIVERSITY OF WYOMING   (United States)

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEXITY CLASSES; ENTROPY RATES; POLYNOMIAL-TIME DIMENSION; RESOURCE BOUNDED DIMENSION;

COMPUTATIONAL COMPLEXITY; FUNCTION EVALUATION; HIERARCHICAL SYSTEMS; POLYNOMIALS; SET THEORY; THEOREM PROVING;

ENTROPY;

EID: 4944254476     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. Effective fractal dimension bibliography. http://www.cs.uwyo.edu/ ~jhitchco/bib/dim.html.
2. E. Allender and R. Rubinstein. P-printable sets. SIAM Journal on Computing, 17:1193-1202, 1988.
3. N. Chomsky and G. A. Miller. Finite state languages. Information and Control, 1:91-112, 1958.
4. J. J. Dai, J. I. Lathrop, J. H. Lutz, and E. Mayordomo. Finite State dimension. Theoretical Computer Science, 310(1-3):1-33, 2004.
5. S. A. Fenner, Gales and supergales are equivalent for defining constructive Hausdorff dimension. Technical Report cs.CC/0208044, Computing Research Repository, 2002.
6. L. Fortnow and J. H. Lutz. Prediction and dimension. Journal of Computer and System Sciences. To appear.
7. A. V. Goldberg and M. Sipser. Compression and ranking. SIAM Journal on Computing, 20(3):524-536, 1991.
8. J. Hartmanis and Y. Yesha. Computation times of NP sets of different densities. Theoretical Computer Science, 34: 17-32, 1984.
9. J. M. Hitchcock. Correspondence principles for effective dimensions. Theory of Computing Systems. To appear.
10. J. M. Hitchcock. Effective Fractal Dimension; Foundations and Applications. PhD thesis, Iowa State University, 2003.
11. J. M. Hitchcock. Fractal dimension and logarithmic loss unpredictability. Theoretical Computer Science, 304(1-3):431-441, 2003.
12. J. M. Hitchcock. Gales suffice for constructive dimension. Information Processing Letters, 86(1):9-12, 2003.
13. J. M. Hitchcock. Small spans in scaled dimension. Technical Report cs.CC/0304030, Computing Research Repository, 2003.
14. J. M. Hitchcock, J. H. Lutz, and E. Mayordomo. Scaled dimension and nonuniform complexity. Journal of Computer and System Sciences. To appear.
15. J. Köbler, U. Schöning, and J. Toran. On counting and approximation. Acta Informatica, 26:363-379, 1989.
16. W. Kuich. On the entropy of context-free languages. Information and Control, 16:173-200, 1970.
17. J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of Computer and System Sciences, 44(2):220-258, 1992.
18. J. H. Lutz. The quantitative structure of exponential time. In L. A. Hemaspaandra and A. L. Selman, editors, Complexity Theory Retrospective II, pages 225-254. Springer-Verlag, 1997.
19. J.H.Lutz. Dimension in complexity classes. SIAM Journal on Computing, 32(5): 1236-1250, 2003.
20. J. H. Lutz. The dimensions of individual strings and sequences. Information and Computation, 187(1):49-79, 2003.
21. J. H. Lutz. Effective fractal dimensions. In Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 81-97. FernUniversität in Hagen, August 2003.
22. E. Mayordomo. Effective Hausdorff dimension. In Proceedings of Foundations of the Formal Sciences III. Kluwer Academic Press. To appear.
23. E. Mayordomo. Contributions to the study of resource-bounded measure. PhD thesis, Universitat Politècnica de Catalunya, 1994.
24. E. Mayordomo. A Kolmogorov complexity characterization of constructive Hausdorff dimension. Information Processing Letters, 84(1):1-3, 2002.
25. C. A. Rogers. Hausdorff Measures. Cambridge University Press, 1998. Originally published in 1970.
26. L. Staiger. Kolmogorov complexity and Hausdorff dimension. Information and Computation, 103:159-94, 1993.
27. L. Staiger. A tight upper bound on Kolmogorov complexity and uniformly optimal prediction. Theory of Computing Systems, 31:215-29, 1998.
28. L. J. Stockmeyer. On approximation algorithms for #P. SIAM Journal on Computing, 14:849-861, 1985.
29. J. Ville. Étude Critique de la Notion de Collectif. Gauthier-Villars, Paris, 1939.