Effective complexity of stationary process realizations

Entropy

Volumn 13, Issue 6, 2011, Pages 1200-1211

  Ay, Nihat ^a,c   Müller, Markus ^a,b   Szkoła, Arleta ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c SANTA FE INSTITUTE   (United States)

Author keywords

Coarse effective complexity; Computable stationary processes; Effective complexity; Kolmogorov complexity; Shannon entropy

Indexed keywords

EID: 79960754171     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e13061200     Document Type: Article

References (16)

1. Ay, N.; Müller, M.; Szkoła, A. Effective complexity and its relation to logical depth. IEEE Trans. Inform. Theory 2010, 56, 4593-4607.
2. Gell-Mann, M.; Lloyd, S. Effective complexity. In Nonextensive Entropy-Interdisciplinary Applications; Gell-Mann, M., Tsallis, C., Eds.; Oxford University Press: New York, NY, USA, 2004; pp. 387-398.
3. Gell-Mann, M.; Lloyd, S. Information measures, effective complexity, and total information. Complexity 1996, 2, 44-52.
4. Rissanen, J. Stochastic complexity in statistical inquiry. In Series in Computer Science 15; World scientific publishing Co.: Singapore, 1988.
5. Gács, P.; Tromp, J.T.; Vitányi, P.M. Algorithmic statistics. IEEE Trans. Inform. Theory 2001, 47, 2443-2463.
6. Vitányi, P.M. Meaningful information. IEEE Trans. Inform. Thoery 2006, 52, 4617-4626.
7. Koppel, M. Structure. In The Universal Turing Machine: A Half-Century Survey; Herken, R., Ed.; Oxford University Press: Oxford, UK, 1988; pp. 235-252.
8. Zurek, W.H. Algorithmic randomness and physical entropy. Phys. Rev. A 1989, 40, 4731-4751.
9. Vereshchagin, N.K.; Vitányi, P.M.B. Kolmogorov's structure function and model selection. IEEE Trans. Inform. Theory 2004, 50, 3265-3290.
10. Antunes, L.; Fortnow, L. Sophistication revisited. Theory Comput. Syst. 2009, 45, 150-161.
11. Bennett, C. Logical depth and physical complexity. In The Universal Turing machine-a Half-Century Survey; Herken, R., Ed.; Oxford University Press: Oxford, UK, 1988.
12. Li, M.; Vitanyi, P. An Introduction to Kolmogorov Complexity and Its Applications; 2nd Ed.; Springer-Verlag: New York, NY, USA, 1997.
13. Kieffer, J. A unified approach to weak universal source coding. IEEE Trans. Inform. Theory 1978, 24, 674-682.
14. Ziv, J. Coding of sources with unknown statistics-I: Probability of encoding error. IEEE Trans. Inform. Theory 1972, 18, 384-389.
15. Cover, T.M.; Thomas, J.A. Elements of Information Theory; John Wiley & Sons: New York, NY, USA, 1991.
16. Brudno, A.A. Entropy and the complexity of the trajectories of a dynamical system. Trans. Moscow Math. Soc. 1983, 2, 127-151.