Finite-state dimension

Theoretical Computer Science

Volumn 310, Issue 1-3, 2004, Pages 1-33

  Dai, Jack J ^a   Lathrop, James I ^b   Lutz, Jack H ^b   Mayordomo, Elvira ^c  

^a PEKING UNIVERSITY   (China)

^b Iowa State University   (United States)

^c UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Bounded depth circuit; Finite state compressor; Finite state dimension; Finite state gambler; Gale; Hausdorff dimension; Information lossless compressor; Martingale; Normal sequence

Indexed keywords

APPROXIMATION THEORY; BINARY SEQUENCES; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; ENTROPY; INFORMATION SCIENCE; THEOREM PROVING;

FINITE-STATE DIMENSIONS;

FINITE AUTOMATA;

EID: 0242440301     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(03)00244-5     Document Type: Article

References (28)

1. Billingsley P. Ergodic Theory and Information. 1965;Wiley, New York.
2. Borel É. Sur les probabilités dénombrables et leurs applications arithmétiques. Rend. Circ. Mat. Palermo. 27:1909;247-271.
3. Cai J., Hartmanis J. On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line. J. Comput. Systems Sci. 49:1994;605-619.
4. Cover T.M., Thomas J.A. Elements of Information Theory. 1991;Wiley, New York, NY.
5. Eggleston H.G. The fractional dimension of a set defined by decimal properties. Quart. J. Math. Oxford Ser. 20:1949;31-36.
6. Falconer K. The Geometry of Fractal Sets. 1985;Cambridge University Press, Cambridge.
7. Feder M. Gambling using a finite state machine. IEEE Trans. Inform. Theory. 37:1991;1459-1461.
8. Hausdorff F. Dimension und äußeres Maß Math. Ann. 79:1919;157-179.
9. D.A. Huffman, Canonical forms for information-lossless finite-state logical machines, IRE Trans. Circuit Theory CT-6 (Special Suppl.) 1959, pp. 41-59, also available in: E.F. Moore (Ed.), Sequential Machine: Selected Papers, Addison-Wesley, Reading, MA, 1964, pp. 866-871.
10. D.A. Huffman, Canonical forms for information-lossless finite-state logical machines, IRE Trans. Circuit Theory CT-6 (Special Suppl.) 1959, pp. 41-59, also available in: E.F. Moore (Ed.), Sequential Machine: Selected Papers, Addison-Wesley, Reading, MA, 1964, pp. 866-871.
11. Johnson D.S. A catalog of complexity classes. van Leeuwen J. A Handbook of Theoretical Computer Science. Vol. A:1990;67-181 Elsevier, Amsterdam.
12. Kelley J.L. A new interpretation of information rate. Bell System Tech. J. 35:1956;917-926.
13. Kohavi Z. Switching and Finite Automata Theory. 2nd Edition:1978;McGraw-Hill, New York.
14. Kurmit A.A. Information-Lossless Automata of Finite Order. 1974;Wiley, New York.
15. Lathrop J.I., Strauss M.J. A universal upper bound on the performance of the Lempel-Ziv algorithm on maliciously-constructed data. Carpentieri B. Compression and Complexity of Sequences '97. 1998;123-135 IEEE Computer Society Press, Silver Spring, MD.
16. Lempel A., Ziv J. Compression of individual sequences via variable rate coding. IEEE Trans. Inform. Theory. 24:1978;530-536.
17. J.H. Lutz, Dimension in complexity classes, SIAM J. Comput., to appear.
18. J.H. Lutz, The dimensions of individual strings and sequences, Inform. Comput., to appear.
19. Ryabko B.Ya. Noiseless coding of combinatorial sources. Problems Inform. Transmission. 22:1986;170-179.
20. Ryabko B.Ya. Algorithmic approach to the prediction problem. Problems Inform. Transmission. 29:1993;186-193.
21. Ryabko B.Ya. The complexity and effectiveness of prediction problems. J. Complexity. 10:1994;281-295.
22. Scheinwald D. On the Lempel-Ziv proof and related topics. Proc. IEEE. 82:1994;866-871.
23. Schnorr C.P., Stimm H. Endliche automaten und zufallsfolgen. Acta Inform. 1:1972;345-359.
24. Shannon C.E. A mathematical theory of communication. Bell System Tech. J. 27:1948;379-423, 623-656.
25. Staiger L. Kolmogorov complexity and Hausdorff dimension. Inform. Comput. 102:1993;159-194.
26. Staiger L. A tight upper bound on Kolmogorov complexity and uniformly optimal prediction. Theory Comput. Systems. 31:1998;215-229.
27. Strauss M.J. Normal numbers and sources for BPP. Theoret. Comput. Sci. 178:1997;155-169.
28. Ziv J. Coding theorem for individual sequences. IEEE Trans. Inform. Theory. 24:1978;405-412.