Kolmogorov complexity and instance complexity of recursively enumerable sets

SIAM Journal on Computing

Volumn 25, Issue 6, 1996, Pages 1123-1143

  Kummer, Martin ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Complete sets; Instance complexity; Kolmogorov complexity; Recursively enumerable sets

Indexed keywords

EID: 0009975816     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794268789     Document Type: Article

References (16)

1. J. BARZDIN, Complexity of programs to determine whether natural numbers not greater than n belong to a recursively enumerable set, Soviet Math. Dokl., 9 (1968), pp. 1251-1254.
2. H. BUHRMAN AND P. ORPONEN, Random strings make hard instances, in Proc. 9th Annual Conference on Structure in Complexity Theory, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 217-222.
3. C. CALUDE, Information and Randomness, Springer-Verlag, Berlin, 1994.
4. G. J. CHAITIN, Information-theoretic characterizations of recursive infinite strings, Theoret. Comput. Sci., 2 (1976), pp. 45-48.
5. R. DOWNEY, C. G. JOCKUSCH, AND M. STOB, Array nonrecursive sets and multiple permitting arguments, in Proc. Recursion Theory Week, K. Ambos-Spies, G. H. Müller, and G. E. Sacks, eds., Lecture Notes in Math. 1432, Springer-Verlag, Berlin, 1990, pp. 141-174.
6. R. DOWNEY, C. G. JOCKUSCH, AND M. STOB, Array nonrecursive sets and genericity, in Directions in Computability Theory, Cambridge University Press, Cambridge, UK, to appear.
7. L. FORTNOW AND M. KUMMER, On resource-bounded instance complexity, Theoret. Comput. Sci., to appear.
8. K. KO, A note on the instance complexity of pseudorandom sets, in Proc. 7th Annual Conference on Structure in Complexity Theory, IEEE Computer Society Press, Los Alamitos, CA, 1992, pp. 327-337.
9. K. KO, P. ORPONEN, U. SCHÖNING, AND O. WATANABE, What is a hard instance of a computational problem?, in Structure in Complexity Theory, A. Selman, ed., Lecture Notes in Comput. Sci. 223, Springer-Verlag, Berlin, 1986, pp. 197-217.
10. M. LI AND P. VITÁNYI, An Introduction to Kolmogorov Complexity and Its Applications, Springer-Verlag, Berlin, 1993.
11. D. W. LOVELAND, A variant of the Kolmogorov concept of complexity, Inform. and Control, 15 (1969), pp. 510-526.
12. P. ODIFREDDI, Classical Recursion Theory, North-Holland, Amsterdam, 1989.
13. P. ORPONEN, On the instance complexity of NP-hard problems, in Proc. 5th Annual Conference on Structure in Complexity Theory, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 20-27.
14. P. ORPONEN, K. KO, U. SCHÖNING, AND O. WATANABE, Instance complexity, J. Assoc. Comput. Mach., 41 (1994), pp. 96-121.
15. R. I. SOARE, Recursively Enumerable Sets and Degrees, Springer-Verlag, Berlin, 1987.
16. J. TROMP, On a conjecture by Orponen + 3, in Descriptive Complexity, R. V. Book, E. Pednault, and D. Wotschke, eds., Dagstuhl-Seminar-Report, vol. 63, IBFI GmbH, Wadern, Germany, 1993, p. 20.