On Kurtz randomness

Theoretical Computer Science

Volumn 321, Issue 2-3, 2004, Pages 249-270

  Downey, Rodney G ^a   Griffiths, Evan J ^a   Reid, Stephanie ^a  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Kolmogorov complexity; Kurtz randomness; Lowness; Randomness

Indexed keywords

COMPUTATIONAL COMPLEXITY; MEASUREMENT THEORY; NUMBER THEORY; SET THEORY; TOPOLOGY;

KOLMOGOROV COMPLEXITY; KURTZ RANDOMNESS; LOWNESS; RANDOMNESS;

RANDOM PROCESSES;

EID: 3242725785     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.03.055     Document Type: Article

References (35)

1. K. Ambos-Spies, A. Kučera, Randomness in computability theory, in: P. Cholak, S. Lempp, M. Lerman, R. Shore (Eds.), Computability Theory and its Applications, Contemporary Mathematics, vol. 257, 2000, pp. 1-14.
2. C. Calude, P. Hertling, B. Khoussainov, Y. Wang, Recursively enumerable reals and Chaitin's Ω number, in: M. Morvan, C. Meinel, D. Krob (Eds.), STACS '98, Springer Lecture Notes in Computer Science, vol. 1373, 1998, pp. 596-606.
3. Chaitin G. A theory of program size formally identical to information theory. J. Assoc. Comput. Mach. 22:1975;329-340.
4. R. Downey, E. Griffiths, On Schnorr randomness, J. Symbolic Logic, to appear.
5. R. Downey, E. Griffiths, G. LaForte, On Schnorr and computable randomness, martingales, and machines, Math. Logic Quart., to appear.
6. A, in preparation.
7. R. Downey, D. Hirschfeldt, Algorithmic Randomness and Complexity, Springer, Berlin, to appear.
8. Downey R., Hirschfeldt D., Nies A. Randomness, computability and density. SIAM J. Comput. 31:2002;1169-1183. (Extended abstract appeared in: A. Ferriera, H. Reichel (Eds.), Symp. Theoretical Aspects of Computer Science, STACS'01 January, 2001, Lecture Notes in Computer Science, Springer, Berlin, 2001, pp. 195-201).
9. Downey R., Hirschfeldt D., Nies A. Randomness, computability and density. SIAM J. Comput. 31:2002;1169-1183. (Extended abstract appeared in: A. Ferriera, H. Reichel (Eds.), Symp. Theoretical Aspects of Computer Science, STACS'01 January, 2001, Lecture Notes in Computer Science, Springer, Berlin, 2001, pp. 195-201).
10. R. Downey, D. Hirschfeldt, A. Nies, F. Stephan, Trivial reals, extended abstract, in: B. Schröder (Eds.), Computability and Complexity in Analysis Malaga (Electronic Notes in Theoretical Computer Science, and proceedings, Weihrauch, FernUniversität, 294-6/2002, July 2002, pp. 37-55. Final version appears in: Proc. 7th and 8th Asian Logic Conferences, World Scientific, Singapore, 2003, pp. 103-131).
11. R. Downey, D. Hirschfeldt, A. Nies, F. Stephan, Trivial reals, extended abstract, in: B. Schröder (Eds.), Computability and Complexity in Analysis Malaga (Electronic Notes in Theoretical Computer Science, and proceedings, Weihrauch, FernUniversität, 294-6/2002, July 2002, pp. 37-55. Final version appears in: Proc. 7th and 8th Asian Logic Conferences, World Scientific, Singapore, 2003, pp. 103-131).
12. S. Kautz, Degrees of random sets, Ph.D. Dissertation, Cornell, 1991.
13. B. Kjos-Hanssen, A. Nies, F. Stephan, On a question of Ambos-Spies and Kučera, to appear.
14. 1 -classes and complete extensions of PA, in: H. Ebbinghaus, G. Müller, G. Sacks (Eds.), Recursion Theory Week, Lecture Notes in Mathematics, vol. 1141, Springer, Berlin, 1985, pp. 245-259.
15. Kučera A., Slaman T. Randomness and recursive enumerability. SIAM J. Comput. 31:2001;199-211.
16. Kučera A., Terwijn S. Lowness for the class of random sets. J. Symbolic Logic. 64:1999;1396-1402.
17. Kurtz S. Notions of weak genericity. J. Symbolic Logic. 48:1983;764-770.
18. S. Kurtz, Randomness and genericity in the degrees of unsolvability, Ph.D. Thesis, University of Illinois at Urbana, 1981.
19. Levin L.A. On the notion of a random sequence. Soviet Math. Dokl. 14:1973;1413-1416.
20. Levy P. Theorie de l'Addition des Variables Aleantoires. 1937;Gauthier-Villars, Paris.
21. Li, Ming, P. Vitanyi, Kolmogorov Complexity and its Applications, Springer, Berlin, 1993.
22. Martin-Löf P. The definition of random sequences. Inform. Control. 9:1966;602-619.
23. A. Nies, Reals which compute little, submitted.
24. A. Nies, Lowness properties of reals and randomness, in preparation.
25. B. Kjos-Hanssen, F. Stephan, A. Nies, On a question of Ambos-Spies and Kučera, to appear.
26. Schnorr C.P. Zufälligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics. vol. 218:1971;Springer, Berlin.
27. Schnorr C.P. A unified approach to the definition of a random sequence. Math. Systems Theory. 5:1971;246-258.
28. C.P. Schnorr, A survey of the theory of random sequences, in: Basic Problems in Methodology and Linguistics, D. Reidel, Dordrecht, Holland, 1977, pp. 193-210.
29. Soare R. Recursively Enumerable Sets and Degrees. 1987;Springer, Berlin.
30. Terwijn S., Zambella D. Algorithmic randomness and lowness. J. Symbolic Logic. 66:2001;1199-1205.
31. M. van Lambalgen, Random sequences, Ph.D. Dissertation, University of Amsterdam, 1987.
32. Ville J. Ětude Critique de la Concept du Collectif. 1939;Gauthier-Villars, Paris.
33. von Mises R. Grundlagen der Wahrscheinlichkeitsrechnung. Math. Z. 5:1919;52-99.
34. Y. Wang, Randomness and complexity, Ph.D. Dissertation, University of Heidelberg, 1996.
35. Weihrauch K. Computability. 1987;Springer, Berlin.