Pushdown dimension

Theoretical Computer Science

Volumn 381, Issue 1-3, 2007, Pages 105-123

  Doty, David ^a   Nichols, Jared ^a  

^a Iowa State University   (United States)

Author keywords

Finite state; Martingale; Pushdown; Resource bounded dimension

Indexed keywords

COMPUTABILITY AND DECIDABILITY; COMPUTATIONAL METHODS; COMPUTER SCIENCE; FINITE AUTOMATA;

COMPUTATIONAL INFORMATION DENSITY; INFINITE SEQUENCES; PUSHDOWN; RESOURCE BOUNDED DIMENSION;

INFORMATION ANALYSIS;

EID: 34547175817     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2007.04.005     Document Type: Article

References (42)

1. K. Ambos-Spies, W. Merkle, J. Reimann, F. Stephan, Hausdorff dimension in exponential time, in: Proceedings of the 16th IEEE Conference on Computational Complexity, CCC'2001, June 18-21, 2001, Chicago, Illinois, 2001, pp. 210-217
2. K.B. Athreya, J.M. Hitchcock, J.H. Lutz, E. Mayordomo, Effective strong dimension, algorithmic information, and computational complexity. SIAM Journal on Computing (in press). Preliminary version appeared in V. Diekert and M. Habib (Eds.), Proceedings of the 21st International Symposium on Theoretical Aspects of Computer Science, Springer Lecture Notes in Computer Science, March 25-27, 2004, Montpellier, France, 2004, pp. 632-643
3. Bourke C., Hitchcock J.M., and Vinodchandran N.V. Entropy rates and finite-state dimension. Theoretical Computer Science 349 3 (2005) 392-406
4. Champernowne D.G. The Construction of Decimals Normal in the Scale of Ten. J. London Math. Soc. 2 8 (1933) 254-260
5. Dai J.J., Lathrop J.I., Lutz J.H., and Mayordomo E. Finite-state dimension. Theoretical Computer Science 310 1-3 (2004) 1-33
6. D. Doty, Every sequence is decompressible from a random one, in: Arnold Beckmann, U. Berger, B. Löwe, and J.V. Tucker (Eds.), Logical Approaches to Computational Barriers, Proceedings of the Second Conference on Computability in Europe, CiE 2006, Swansea, UK, July 2006
7. D. Doty, Dimension extractors and optimal decompression. Theory of Computing Systems (in press). Special issue of invited papers from Computability in Europe 2006
8. D. Doty, P. Moser, Finite-state dimension and lossy decompressors. Technical Report cs.CC/0609096, Computing Research Repository, 2006
9. Falconer K. The Geometry of Fractal Sets (1985), Cambridge University Press
10. Feder M. Gambling using a finite-state machine. IEEE Transcations on Information Theory 37 (1991) 1459-1461
11. Fortnow L., and Lutz J.H. Prediction and dimension. Journal of Computer and System Sciences 70 4 (2005) 570-589
12. Fortnow L., Hitchcock J.M., Pavan A., Vinodchandran N.V., and Wang F. Extracting Kolmogorov complexity with applications to dimension zero-one laws. Proceedings of the 33rd International Colloquium on Automata, Languages, and Programming, July 10-14, 2006, Venice, Italy. Lecture Notes in Computer Science vol. 4051 (2006), Springer-Verlag 335-345
13. Glaßer C., Ogihara M., Pavan A., Selman A., and Zhang L. Autoreducibility, mitoticity, and immunity. Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science (2005), Springer-Verlag 387-398
14. Gu X. A note on dimensions of polynomial size circuits. Theoretical Computer Science 359 1-3 (2006) 176-187
15. X. Gu, J.H. Lutz, Dimension characterizations of complexity classes. Computational Complexity (in press)
16. Hausdorff F. Dimension und äußeres Maß. Mathematische Annalen 79 (1919) 157-179
17. J.M. Hitchcock, Effective fractal dimension: foundations and applications. Ph.D. Dissertation, Iowa State University, 2003
18. Hitchcock J.M. Fractal dimension and logarithmic loss unpredictability. Theoretical Computer Science 304 1-3 (2003) 431-441
19. Hitchcock J.M. MAX3SAT is exponentially hard to approximate if NP has positive dimension. Theoretical Computer Science 289 1 (2002) 861-869
20. Hitchcock J.M. Online learning and resource-bounded dimension: Winnow yields new lower bounds for hard sets. SIAM Journal on Computing 36 6 (2007) 1696-1708
21. Hitchcock J.M., and Pavan A. Hardness hypotheses, derandomization, and circuit complexity. Proceedings of the 24th Conference on Foundations of Software Technology and Theoretical Computer Science (2004), Springer-Verlag 336-347
22. J.M. Hitchcock, A. Pavan, N.V. Vinodchandran, Partial bi-immunity, scaled dimension, and NP-completeness. Theory of Computing Systems (in press)
23. Hitchcock J.M., Lutz J.H., and Mayordomo E. Scaled dimension and nonuniform complexity. Journal of Computer and System Sciences 69 2 (2004) 97-122
24. Hopcroft J.E., and Ullman J.D. Introduction to Automata Theory, Languages, and Computation (1979), Addison-Wesley, New York, NY
25. Kuich W., and Salomaa A. Semirings, Automata, Languages. EATCS Monographs On Theoretical Computer Science vol. 5 (1985)
26. Lathrop J.I., and Strauss M. A universal upper bound on the performance of the Lempel-Ziv algorithm on maliciously-constructed data. Proceedings of the Compression and Complexity of Sequences. June 11-13, 1997, Salerno, Italy (1997), IEEE 123-135
27. López-Valdés M., and Mayordomo E. Dimension is compression. Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science. MFCS'05. Lecture Notes in Computer Science vol. 3618 (2005), Springer-Verlag 676-685
28. Lutz J.H. Dimension in complexity classes. SIAM Journal on Computing 32 5 (2003) 1236-1259
29. Lutz J.H. The dimensions of individual strings and sequences. Information and Computation 187 1 (2003) 49-79
30. Mayordomo E. A Kolmogorov complexity characterization of constructive Hausdorff dimension. Information Processing Letters 84 1 (2002) 1-3
31. Merkle W., and Reimann J. On selection functions that do not preserve normality. Theory of Computing Systems 39 5 (2006) 685-697
32. P. Moser, BPP has effective dimension at most 1/2 unless BPP = EXP. Technical Report TR03-029, Electronic Colloquium on Computational Complexity, 2003
33. P. Moser, Derandomization and quantitative complexity. Ph.D. Thesis, Université de Genève, 2004
34. Moser P. Generic density and small span theorem. Proceedings of the 15th International Symposium on Fundamentals of Computation Theory (2005), Springer-Verlag 92-102
35. P. Moser, Martingale families and dimension in P, in: A. Beckmann, U. Berger, B. Löwe, and J.V. Tucker (Eds.), Logical Approaches to Computational Barriers, Proceedings of the Second Conference on Computability in Europe, CiE 2006, July 2006, Swansea, UK, 2006
36. J. Nichols, Pushdown gamblers and pushdown dimension, Master's Thesis, Iowa State University, 2004
37. Schnorr C., and Stimm H. Endliche Automaten und Zufallsfolgen. Acta Informatica 1 (1972) 345-359
38. Sheinwald D., Lempel A., and Ziv J. On encoding and decoding with two-way head machines. Information and Computation 116 1 (1995) 128-133
39. Staiger L. Weighted finite automata and metrics in Cantor space. Journal of Automata, Languages and Combinatorics 8 2 (2003) 353-360
40. Sullivan D. Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups. Acta Mathematica 153 (1984) 259-277
41. Tricot C. Two definitions of fractional dimension. Mathematical Proceedings of the Cambridge Philosophical Society 91 (1982) 57-74
42. Ziv J., and Lempel A. Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory 24 5 (1978) 530-536