The Kolmogorov-Loveland stochastic sequences are not closed under selecting subsequences

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

Volumn 2380 LNCS, Issue , 2002, Pages 390-400

  Merkle, Wolfgang ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; COMPUTATIONAL COMPLEXITY;

KOLMOGOROV; SELECTION RULES;

STOCHASTIC SYSTEMS;

EID: 0042919186     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45465-9_34     Document Type: Conference Paper

References (22)

1. K. Ambos-Spies and E. Mayordomo. Resource-bounded measure and randomness. In Complexity, Logic, and Recursion Theory, Marcel Dekker, Inc, 1997.
2. K. Ambos-Spies and A. Kuĉera. Randomness in Computability Theory. In P. Cholak et al. (eds.), Computability Theory: Current Trends and Open Problems, Contemporary Mathematics 257:1-14, American Mathematical Society, 2000.
3. J.L. Balcázar, J. Díaz and J. Gabarró. Structural Complexity, Vol. I and II. Springer, 1995 and 1990.
4. A. Church. On the concept of a random number. Bulletin of the AMS, 46:130-135,1940.
5. R. P. Daley. Minimal-program complexity of pseudo-recursive and pseudo-random sequences. Mathematical Systems Theory, 9:83-94,1975.
6. W. Feller. An Introduction to Probability Theory and Its Applications. Vol. I, third edition, revised printing. John Wiley, 1968.
7. A. N. Kolmogorov. On tables of random numbers. Sankhyā, Ser. A, 25:369-376, 1963.
8. A. N. Kolmogorov and V. A. Uspensky. Algorithms and randomness. Theory of Probability and its Applications 32:389-412, 1987.
9. M. van Lambalgen. Random sequences, Doctoral dissertation, University of Amsterdam, Amsterdam, 1987.
10. M. Li and P. Vitányi An Introduction to Kolmogorov Complexity and Its Applications, second edition, Springer, 1997.
11. D. W. Loveland. A new interpretation of the von Mises' concept of random sequence. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 12:279-294, 1966.
12. D. W. Loveland. The Kleene hierarchy classification of recursively random sequences. Transactions of the AMS, 125:497-510, 1966.
13. J. H. Lutz and D. L. Schweizer. Feasible reductions to Kolmogorov-Loveland stochastic sequences. Theoretical Computer Science, 225:185-194, 1999.
14. J. H. Lutz. Private Communication, March 2002.
15. An. A. Muchnik, A. L. Semenov, and V. A. Uspensky. Mathematical metaphysics of randomness. Theoretical Computer Science, 207:263-317, 1998.
16. P. Odifreddi. Classical Recursion Theory. Vol. I. North-Holland, Amsterdam, 1989.
17. C. H. Papadimitriou. Computational Complexity. Addison-Wesley Publishing Company, 1994.
18. A. Kh. Shen'. The frequency approach to the definition of the notion of a random sequence (in Russian). Semiotika i Informatika, 18:14-41, 1982.
19. A. Kh. Shen'. On relations between different algorithmic definitions of randomness. Soviet Mathematics Doklady, 38:316-319, 1988.
20. A. Kh. Shen'. Private Communication, November 2001.
21. V. A. Uspensky, A. L. Semenov, and A. Kh. Shen'. Can an individual sequence of zeros and ones be random? Russian Math. Surveys, 45:121-189, 1990.
22. J. Ville, Étude Critique de la Notion de Collectif. Gauthiers-Villars, Paris, 1939