Lowness for the class of schnorr random reals

SIAM Journal on Computing

Volumn 35, Issue 3, 2005, Pages 647-657

  Kjos Hanssen, Bjørn ^a   Nies, André ^b   Stephan, Frank ^c  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Computability theory; Lowness; Randomness; Recursion theory; Schnorr randomness; Turing degrees

Indexed keywords

COMPUTABILITY THEORY; LOWNESS; RANDOMNESS; RECURSION THEORY; SCHNORR RANDOMNESS; TURING DEGREES;

COMPUTABILITY AND DECIDABILITY; COMPUTATION THEORY; TURING MACHINES;

RANDOM PROCESSES;

EID: 33745463530     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539704446323     Document Type: Article

References (16)

1. K. AMBOS-SPIES AND A. KUČERA, Randomness in computability theory, in Computability Theory and Its Applications (Boulder, CO, 1999), Contemp. Math. 257, AMS, Providence, RI, 2000, pp. 1-14.
2. B. BEDREGAL AND A. NIES, Lowness properties of reals and hyper-immunity, in Proceedings of the 10th Workshop on Logic, Language, Information, and Computation, Ouro Preto, Minas Gerais, Brazil, 2003, Electron. Notes Theor. Comput. Sci. 84, Elsevier, 2003, online at http://www.elsevier.nl/locate/entcs/ volume84.html.
3. A. CHURCH, On the concept of a random sequence, Bull. Amer. Math. Soc., 46 (1940), pp. 130-135.
4. R. G. DOWNEY, C. G. JOCKUSCH, JR., AND M. STOB, Array nonrecursive sets and genericity, in Computability, Enumerability, Unsolvability: Directions in Recursion Theory, S. B. Cooper, T. A. Slaman, and S. S. Wainer, eds., London Math. Soc. Lecture Note Ser., Cambridge University Press, Cambridge, UK, 1996, pp. 93-104.
5. S. ISHMUKHAMETOV, Weak recursive degrees and a problem of Spector, Recursion Theory and Complexity (Kazan, 1997), de Gruyter Ser. Log. Appl. 2, de Gruyter, Berlin, 1999, pp. 81-87.
6. B. KJOS-HANSSEN, W. MERKLE, AND F. STEPHAN, Kolmogorov Complexity and the Recursion Theorem, to appear.
7. 0-classes and complete extensions of PA, in Recursion Theory Week (Oberwolfach, 1984), Lecture Notes in Math. 1141, Springer, Berlin, 1985, pp. 245-259.
8. A. KUČERA AND S. TERWIJN, Lowness for the class of random sets, J. Symbolic Logic, 64 (1999), pp. 1396-1402.
9. P. MARTIN-LÖF, The definition of random sequences, Inform, and Control, 9 (1966), pp. 602-619.
10. D. A. MARTIN AND W. MILLER, The degrees of hyperimmune sets, Z. Math. Logik Grundlag. Math., 14 (1968), pp. 159-166.
11. A. NIES, Lowness properties and randomness, Adv. Math., 197 (2005), pp. 274-305.
12. A. NIES, F. STEPHAN, AND S. TERWIJN, Randomness, relativization, and Turing degrees, J. Symbolic Logic, 70 (2005), pp. 515-535.
13. C.-P. SCHNORR, Zufälligkeit und Wahrscheinlichkeit. Eine algorithmische Begründung der Wahrscheinlichkeitstheorie, Lecture Notes in Math. 218, Springer-Verlag, Berlin, 1971.
14. S. TERWIJN AND D. ZAMBELLA, Computational randomness and lowness, J. Symbolic Logic, 66 (2001), pp. 1199-1205.
15. M. VAN LAMBALGEN, The axiomatization of randomness, J. Symbolic Logic, 55 (1990), pp. 1143-1167.
16. D. ZAMBELLA, On Sequences with Simple Initial Segments, ILLC Technical Report ML 1990-05, University of Amsterdam, Amsterdam, The Netherlands, 1990.