Lowness properties and randomness

Advances in Mathematics

Volumn 197, Issue 1, 2005, Pages 274-305

  Nies, André ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

K trivial; Kolmogorov prefix complexity; Low for random; Randomness

Indexed keywords

EID: 24644511669     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2004.10.006     Document Type: Article

References (30)

1. K. Ambos-Spies C.G. Jockusch jr R.A. Shore R.I. Soare An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees Trans. Amer. Math. Soc. 281 1984 109-128
2. K. Ambos-Spies A. Kucera Randomness in computability theory current trend and open problem in: P. Cholak S. Lempp M. Lerman R. Shore (Eds.) Computability Theory and Its Applications Current Trends and Open Problems 2000 American Mathematical Society Providence, RI
3. A. Nies, B. Bedregal, Lowness properties of reals and hyper-immunity, in: Wollic 2003, Electronic Notes in Theoretical Computer Science, vol. 84, Elsevier, Amsterdam, 2003. http://www.elsevier.nl/locate/entcs/ volume84.html
4. C. Calude, Information and randomness, Monographs in Theoretical Computer Science, An EATCS Series. Springer, Berlin, 1994. An algorithmic perspective, With forewords by Gregory J. Chaitin and Arto Salomaa.
5. C.S. Calude R.J. Coles Program-size complexity of initial segments and domination reducibility in: Jewels are Forever 1999 Springer Berlin 225-237
6. G. Chaitin A theory of program size formally identical to information theory J. Assoc. Comput. Mach. 22 1975 329-340
7. G. Chaitin Information-theoretical characterizations of recursive infinite strings Theoret. Comput. Sci. 2 1976 45-48
8. P. Cholak M. Groszek T. Slaman An almost deep degree J. Symbolic Logic 66 2 2001 881-901
9. R.G. Downey, D.R. Hirschfeldt, A. Nies, F. Stephan, Trivial reals, in: Proceedings of the 7th and 8th Asian Logic Conferences, Singapore University Press, Singapore, 2003, pp. 103-133.
10. R. Downey, D. Hirschfeldt, A. Nies, S. Terwijn, Calibrating randomness, Bull. Symbolic Logic., to appear.
11. D. Hirschfeldt, A. Nies, F. Stephan, Random Oracles, to appear.
12. C.G. Jockusch Jr R.A. Shore Pseudo-jump operators I: The r.e. case Trans. Amer. Math. Soc. 275 1983 599-609
13. B. Kjos-Hanssen, F. Stephan, A. Nies, Lowness for the class of Schnorr random sets, to appear.
14. A. Kucera On relative randomness Ann. Pure Appl. Logic 63 1993 61-67
15. A. Kucera S. Terwijn Lowness for the class of random sets J. Symbolic Logic 64 1999 1396-1402
16. P. Martin-Löf The definition of random sequences Inform. and Control 9 1966 602-619
17. J. Miller, L. Yu, On initial segment complexity and degrees of randomness, to appear.
18. W. Miller D.A. Martin The degree of hyperimmune sets Z. Math. Logik Grundlag. Math. 14 1968 159-166
19. A.A. Muchnik A.L. Semenov V.A. Uspensky Mathematical metaphysics of randomness Theoret. Comput. Sci. 207 2 1998 263-317
20. A. Nies, Computability and randomness, to appear.
21. A. Nies, Ideals in the recursively enumerable degrees, to appear.
22. A. Nies, Reals which compute little, to appear.
23. Gerald E. Sacks, Degrees of Unsolvability, Annals of Mathematical Studies, vol. 55, Princeton University Press, Princeton, NJ, 1963.
24. C.-P. Schnorr, Zufälligkeit und Wahrscheinlichkeit. Eine algorithmische Begründung der Wahrscheinlichkeitstheorie, Lecture Notes in Mathematics, vol. 218, Springer, Berlin, 1971.
25. T.A. Slaman, Aspects of the Turing jump, in: Logic Colloquium 2000, Lecture Notes in Logic, to appear.
26. T. Slaman, R. Solovay, When oracles do not help, in: Fourth Annual Conference on Computational Learning Theory, Morgan Kaufman, Los Altos, CA, 1991, pp. 379-383.
27. R. Soare Recursively Enumerable Sets and Degrees, Perspectives in Mathematical Logic, Omega Series 1987 Springer Heidelberg
28. R. Solovay, Draft of a paper (or series of papers) on chaitin's work, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1975, 215p.
29. S. Terwijn D. Zambella Algorithmic randomness and lowness J. Symbolic Logic 66 2001 1199-1205
30. D. Zambella, On sequences with simple initial segments, ILLC Technical Report ML 1990-05, University Amsterdam, 1990.