On the construction of effective random sets

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

Volumn 2420, Issue , 2002, Pages 568-580

  Merkle, Wolfgang ^a   Mihailović, Nenad ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY;

AUTOREDUCIBILITY; COMPUTABLY ENUMERABLE; RANDOM SET; TRUTH TABLES;

SET THEORY;

EID: 84957015740     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45687-2_47     Document Type: Conference Paper

References (23)

1. K. Ambos-Spies and A. Kučera. Randomness in computability theory. In P. A. Cholak et al. (eds.), Computability Theory and Its Applications. Current Trends and Open Problems. Contemporary Mathematics 257:1–14, American Mathematical Society (AMS), 2000.
2. K. Ambos-Spies and E. Mayordomo. Resource-bounded measure and randomness. In A. Sorbi (ed.), Complexity, Logic, and Recursion Theory, p. 1-47. Dekker, New York, 1997.
3. T. M. Apostol. Mathematical Analysis, third edition. Addison Wesley, 1978.
4. J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I, Springer, 1995.
5. C. Calude, Information and Randomness, Springer-Verlag, 1994.
6. C. S. Calude. A characterization of c.e. random reals. Theoretical Computer Science 271:3-14, 2002.
7. T. Ebert. Applications of Recursive Operators to Randomness and Complexity. Ph.D. Thesis, University of California at Santa Barbara, 1998.
8. T. Ebert and H. Vollmer. On the autoreducibility of random sequences. In: M. Nielsen and B. Rovan (eds.), Mathematical Foundations of Computer Science 2000, Lecture Notes in Computer Science 1893:333–342, Springer, 2000.
9. T. Ebert and W. Merkle. Autoreducibility of random sets: a sharp bound on the density of guessed bits. Mathematical Foundations of Computer Science 2002, this volume.
10. P. Gács. Every sequence is reducible to a random one. Information and Control 70:186–192, 1986.
11. A. Kučera. Measure, Π0 1 -classes and complete extensions of PA. In: H.-D. Ebbinghaus et al. (eds.), Recursion Theory Week. Lecture Notes in Mathematics 1141:245-259, Springer, 1985.
12. A. Kučera. On the use of diagonally nonrecursive functions. In: H.-D. Ebbinghaus et al. (eds.), Logic Colloquium’87. Studies in Logic and the Foundations of Mathematics 129:219-239, North-Holland, 1989.
13. M. Li and P. Vitányi. An Introduction to Kolmogorov Complexity and Its Applications, second edition. Springer, 1997.
14. J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of Computer and System Sciences, 44:220–258, 1992.
15. J. H. Lutz. The quantitative structure of exponential time. In L. A. Hemaspaandra and A. L. Selman (eds.), Complexity Theory Retrospective II, p. 225–260, Springer, 1997.
16. P. Martin-Löf. The definition of random sequences. Information and Control 9(6):602–619, 1966.
17. E. Mayordomo. Contributions to the Study of Resource-Bounded Measure. Doctoral dissertation, Universitat Politècnica de Catalunya, Barcelona, Spain, 1994.
18. P. Odifreddi. Classical Recursion Theory. North-Holland, Amsterdam, 1989.
19. C.-P. Schnorr. A unified approach to the definition of random sequences. Mathematical Systems Theory, 5:246–258, 1971.
20. C.-P. Schnorr. Zufälligkeit und Wahrscheinlichkeit. Lecture Notes in Mathematics 218, Springer, 1971.
21. R. I. Soare. Recursively Enumerable Sets and Degrees. Springer, 1987.
22. S. A. Terwijn. Computability and Measure. Doctoral dissertation, Universiteit van Amsterdam, Amsterdam, Netherlands, 1998.
23. B. A. Trakhtenbrot, On autoreducibility. Soviet Math. Doklady, 11:814-817, 1970.