Dimension is compression

Lecture Notes in Computer Science

Volumn 3618, Issue , 2005, Pages 676-685

  López Valdés, María ^a   Mayordomo, Elvira ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; INFORMATION THEORY; POLYNOMIALS;

COMPLEXITY CLASSES; CONSTRUCTIVE DIMENSION; FRACTAL DIMENSION;

FRACTALS;

EID: 26844471761     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11549345_58     Document Type: Conference Paper

References (16)

1. K. Ambos-Spies, W. Merkle, J. Reimann, and F. Stephan. Hausdorff dimension in exponential time. In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210-217, 2001.
2. K. B. Athreya, J. M. Hitchcock, J. H. Lutz, and E. Mayordomo. Effective strong dimension in algorithmic information and computational complexity. In Proceedings of the Twenty-First Symposium on Theoretical Aspects of Computer Science, volume 2996 of Lecture Notes in Computer Science, pages 632-643. Springer-Verlag, 2004.
3. R. Beigel, L. Fortnow, and F. Stephan. Infinitely-often autoreducible sets. In Proceedings of the 14th Annual International Symposium on Algorithms and Computation, volume 2906 of Lecture Notes in Computer Science, pages 98-107. Springer-Verlag, 2003.
4. H. Buhrman and L. Longpré. Compressibility and resource bounded measure. SIAM Journal on Computing, 31(3):876-886, 2002.
5. J. M. Hitchcock. MAX3SAT is exponentially hard to approximate if NP has positive dimension. Theoretical Computer Science, 289(1):861-869, 2002.
6. J. M. Hitchcock. Effective Fractal Dimension: Foundations and Applications. PhD thesis, Iowa State University, 2003.
7. J. M. Hitchcock. Fractal dimension and logarithmic loss unpredictability. Theoretical Computer Science, 304(1-3):431-441, 2003.
8. J. M. Hitchcock and N. V. Vinodchandran. Dimension, entropy rates, and compression. In Proceedings of the 19th IEEE Conference on Computational Complexity, pages 174-183, 2004.
9. J C. Kieffer and En hui Yang. Grammar based codes: A new class of universal lossless source codes. IEEE Transactions on Information Theory, 46:737-754, 2000.
10. A. Lempel and J. Ziv. A universal algortihm for sequential data compression. IEEE Transaction on Information Theory, 23:337-343, 1977.
11. A. Lempel and J. Ziv. Compression of individual sequences via variable rate coding. IEEE Transaction on Information Theory, 24:530-536, 1978.
12. J. H. Lutz. Effective fractal dimensions. Mathematical Logic Quarterly. To appear. Preliminary version appeared in Computability and Complexity in Analysis, volume 302 of Informatik Berichte, pages 81-97. FernUniversität in Hagen, August 2003.
13. J. H. Lutz. Dimension in complexity classes. SIAM Journal on Computing, 32:1236-1259, 2003.
14. J. H. Lutz. The dimensions of individual strings and sequences. Information and Computation, 187:49-79, 2003.
15. E. Mayordomo. A Kolmogorov complexity characterization of constructive Hausdorff dimension. Information Processing Letters, 84(1):1-3, 2002.
16. E. Mayordomo. Effective Hausdorff dimension. In Classical and New Paradigms of Computation and their Complexity Hierarchies, Papers of the conference "Foundations of the Formal Sciences III", volume 23 of Trends in Logic, pages 171-186. Kluwer Academic Press, 2004.