Algorithmic complexity and stochastic properties of finite binary sequences

Computer Journal

Volumn 42, Issue 4, 1999, Pages 315-317

  V'yugin, V V ^a  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; PROBABILITY; RANDOM PROCESSES; STATISTICAL METHODS;

BERNOULLI SEQUENCES; KOLMOGOROV COMPLEXITY;

COMPUTATIONAL COMPLEXITY;

EID: 0032684824     PISSN: 00104620     EISSN: None     Source Type: Journal    
DOI: 10.1093/comjnl/42.4.294     Document Type: Article

References (50)

1. Kolmogorov, A. N. (1965) Three approaches to the quantitative definition of information. Prob. Inform. Transmission, 1, 4-7.
2. Kolmogorov, A. N. (1968) The logical basis for information theory and probability theory. IEEE Trans. Inf. Theory, IT 14, 662-664.
3. Cover, T. M., Gâcs, P. and Gray, R. M. (1989) Kolmogorov's contributions to information theory and algorithmic complexity. Probab., 17, 840-865.
4. Solomonoff, R. J. (1964) A formal theory of inductive inference I, II. Inform. Control, 7, 1-22, 224-254.
5. Chaitin, G. J. (1966) On the length of programs for computing binary sequences. J. Assoc. Compitt. Mach., 13, 547-569.
6. Chaitin, G. J. (1969) On the length of programs for computing binary sequences: statistical considerations. J. Assoc. Comput. Mach., 16, 145-159.
7. Zvonkin, A. K. and Levin, L. A. (1970) The complexity of finite objects and the algorithmic concepts of information and randomness. Russ. Math. Sur\\, 25, 83-124.
8. V'yugin, V. V. (1981) Algorithmic entropy (complexity) of finite objects, and its application to defining randomness and quantity of information. Semiotika and Infonnatica, 16, 14-43. In Russian.
9. Translated into English in (1994) Selecta Mathematica, formerly Sovietica, 13, 357-389.
10. Kolmogorov, A. N. and Uspensky, V. A. (1987) Algorithms and randomness. Theory Probab. Applic., 32, 389-412.
11. Li, M. and Vitânyi, P. (1988) Kolmogorovskaya slozhnost' dvadsat' let spustia. Usp. Math. Nauk, 43, 129-166, in Russian.
12. Uspensky, V. A., Semenov, A. L. and Shen, A. K. (1990) Can an individual sequence of zeros and ones be random? Russ. Math. Sun:, 45, 121-189.
13. Uspensky, V. A. and Shen, A. (1996) Relations between varieties of Kolmogorov complexities. Math. Systems Theory, 29, 271-292.
14. Chaitin, G. J. (1987) Algorithmic Information Theory. Cambridge University Press, Cambridge.
15. Lambalgen, M. (1987) Random Sequences. Academish Proefshri't, Amsterdam.
16. Li, M. and Vitânyi, P. (1997) An Introduction to Kolmogorov Complexity and Its Applications. Springer, New York.
17. Kolmogorov, A. N. (1963) On tables of random numbers. Sankhyaâ, The Indian J. Stat., A 25, 369-376.
18. Rogers, H. (1967) Theory of Recursive Functions and Effective Computability. McGraw Hill, New York.
19. Uspensky, V. A. and Semenov, A. L. ( 1993) Algorithms: Main Ideas and Applications. Kluwer, Dordrecht.
20. Also in Ershov, A. P. and Knuth, D. E. (eds) (1981), Lect. Notes Comput. Sei., Vol. 122, pp. 100-234. Springer, New York.
21. Kolmogorov, A. N. (1983) Combinatorial basis of information theory and probability theory. Russ. Math. Sun'., 38, 29-40.
22. Gâcs, P. and Körner, J. (1973) Common information is far less than mutual information. Prob. Control, and Inform. Theory, 2, 149-162.
23. Muchnik, A. A. (1998) On common information. Theor. Comp.ScL, 207, 319-328.
24. Asarin, E. A. (1987) Some properties of Kolmogorov 5 random finite sequences. SIAM Theory Probab. Appl, 32, 507-508.
25. Li, M. and Vitdnyi, P. (1994) Statistical properties of finite sequences with high Kolmogorov complexity. Math. Systems Theory, 27, 365-376.
26. Vovk, V. G. (1993) A logic of probability, with application to the foundations of statistics. J. R. Statist. Soc., B 55, 317-351.
27. Dawid, A. P. and Vovk, V. G. (1997) Prequential probability: principles and properties. Bernoulli, 3, 1-38.
28. Shen, A. K. (1983) The concept of (a, 0)-stochasticity in the Kolmogorov sense and its properties. Sov. Math.-Dokl., 28, 295-299.
29. V'yugin, V. V. (1987) On the defect of randomness of a finite object with respect to measures with given complexity bounds. SIAM Theory Probab. Appl., 32, 508-512.
30. Levin, L. A. (1974) Laws of information conservation (nongrowth) and aspects of the foundation of probability theory. Prob. Inform. Transmission, 10, 206-210.
31. Gdcs, P. (1974) On the symmetry of algorithmic information. Sov. Math. Dokl. 15, 1477-1480.
32. Levin, L. A. (1976) Various measures of complexity for finite objects (axiomatic description). Sov. Math.-Dokl., 17, 522-526.
33. Chaitin, G. J. (1975) A theory of program size formally identical to information theory. J. Assoc. Comput. Mach., 22, 329-340.
34. Chaitin, G. J. (1977) Algorithmic information theory. IBM J. Res. Develop., 21, 350-359.
35. Solomonoff, R. J. (1978) Complexity-based induction systems: Comparisons and convergence theorems. IEEE Trans. Inform. Theory, IT-24,422-432.
36. Leung-Yan-Chrong, S. K. and Cover, T. M. (1978) Some equivalences between Shannon entropy and Kolmogorov complexity. IEEE. Trans. Inform. Theor); IT-24, 331-338.
37. Wallace, C. S. and Freeman, P. R. (1987) Estimation and inference by compact coding. J. R. Statist. Soc., 49, 240-265.
38. Rissanen, J. (1983) A universal prior for integers and estimation by minimum description length. Ann. Statist., 11, 416-431.
39. Rissanen, J. (1985) Minimum description length principle. In Kotz, S. and Johnson, N. L. (eds), Encyclopedia of Statistical Sciences, Vol. 5, pp. 523-527. Wiley, New York.
40. Vovk, V. G. (1995) Minimum description length estimators under the optimal coding scheme. In Vitanyi, P. (ed.), Computational learning theory. Lect. Notes Comp. Sei., 904, 237-251.
41. Vovk, V. G. ( 1997) Learning about parameter of the Bernoulli model. J. Comp. Syst. Sei., 55, 96-104.
42. Levin, L. A. (1973) On the notion of random sequence. Sov. Math.-Dokl, 14, 1413-1416.
43. Martin-Löf, P. (1966) The definition of random sequences. Inform. Contr., 9, 602-619.
44. Vovk, V. G. (1986) On the concept of the Bernoulli property. Russ. Math. Sun:, 41, 247-248.
45. Schervish, M. J. (1995) Theory of Statistics. Springer, New York.
46. Levin, L. A. (1984) Randomness conservation inequalities; information and independence in mathematical theories. Inform. Contr., 61, 15-37.
47. Levin, L. A. (1973) Universal search problems. Prob. Inform. Transmission, 9, 265-266.
48. Gurevich, Y. (1988) The logic in computer science column. Bull. European Assoc. Tlieor. Comp. Sei., 35, 71-82.
49. Kolmogorov, A. N. and Uspensky, V. A. (1958) To the definition of an algorithm. Usp. Math. Nauk, 13, 3-28 (Russian);
50. English translation in AMS Translations, 21 (1963), 217-245.