Scaled dimension and nonuniform complexity

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2719, Issue , 2003, Pages 278-290

  Hitchcock, John M ^a   Lutz, Jack H ^a   Mayordomo, Elvira ^b  

^a Iowa State University   (United States)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY;

COMPLEXITY CLASS; DECISION PROBLEMS; FRACTAL STRUCTURES; HAUSDORFF DIMENSION; KOLMOGOROV COMPLEXITY; NONUNIFORM COMPLEXITY; RESOURCE-BOUNDED DIMENSION; RESOURCE-BOUNDED MEASURE;

FRACTAL DIMENSION;

EID: 35248853282     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45061-0_24     Document Type: Article

References (20)

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, algorithmic information, and computational complexity. Technical Report cs.CC/0211025, Computing Research Repository, 2002.
3. H.G. Eggleston. The fractional dimension of a set defined by decimal properties. Quarterly Journal of Mathematics, Oxford Series 20:31-36, 1949.
4. K. Falconer. Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, 1990.
5. L. Fortnow and J. H. Lutz. Prediction and dimension. In Proceedings of the 15th Annual Conference on Computational Learning Theory, pages 380-395, 2002.
6. F. Hausdorff. Dimension und äusseres Mass. Mathematische Annalen, 79:157-179, 1919.
7. J. M. Hitchcock. Fractal dimension and logarithmic loss unpredictability. Theoretical Computer Science. To appear.
8. J. M. Hitchcock. MAX3SAT is exponentially hard to approximate if NP has positive dimension. Theoretical Computer Science, 289(1):861-869, 2002.
9. D. W. Juedes and J. H. Lutz. Completeness and weak completeness under polynomial-size circuits. Information and Computation, 125:13-31, 1996.
10. P. Lévy. Théorie de l'Addition des Variables Aleatoires. Gauthier-Villars, 1937 (second edition 1954).
11. J. H. Lutz. Dimension in complexity classes. SIAM Journal on Computing. To appear. Available as Technical Report cs.CC/0203016, Computing Research Repository, 2002.
12. J. H. Lutz. The dimensions of individual strings and sequences. Information and Computation. To appear. Available as Technical Report cs.CC/0203017, Computing Research Repository, 2002.
13. J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of Computer and System Sciences, 44:220-258, 1992.
14. J. H. Lutz. Resource-bounded measure. In Proceedings of the 13th IEEE Conference on Computational Complexity, pages 236-248, 1998.
15. C. A. Rogers. Hausdorff Measures. Cambridge University Press, 1998. Originally published in 1970.
16. C. P. Schnorr. Klassifikation der Zufallsgesetze nach Komplexität und Ordnung. Z. Wahrscheinlichkeitstheorie verw. Geb., 16:1-21, 1970.
17. C. P. Schnorr. A unified approach to the definition of random sequences. Mathematical Systems Theory, 5:246-258, 1971.
18. C. P. Schnorr. Zufälligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics, 218, 1971.
19. C. P. Schnorr. Process complexity and effective random tests. Journal of Computer and System Sciences, 7:376-388, 1973.
20. J. Ville. Étude Critique de la Notion de Collectif. Gauthier-Villars, Paris, 1939.