On the structure of degrees of inferability

Journal of Computer and System Sciences

Volumn 52, Issue 2, 1996, Pages 214-238

  Kummer, Martin ^a   Stephan, Frank ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING; COMPUTER SYSTEMS; FORMAL LANGUAGES; INFERENCE ENGINES; LEARNING SYSTEMS; TURING MACHINES;

DEGREES OF INFERABILITY; INFERENCE MACHINES; ORACLE;

RECURSIVE FUNCTIONS;

EID: 0030129211     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1996.0018     Document Type: Article

References (27)

1. L. Adleman and M. Blum, Inductive inference and unsolvability, J. Symbolic Logic 56 (1991), 891-900.
2. R. Beigel, "Query-Limited Reducibilities," Ph.D. thesis, Stanford University, 1987.
3. R. Beigel, W. Gasarch, J. Gill, and J. Owings, Terse, superterse and verbose sets, Inform. and Comput. 103 (1993), 68-85.
4. R. Beigel, M. Kummer, and F. Stephan, Quantifying the amount of verboseness, Inform. and Comput. 120 (1995), 304-314.
5. L. Blum and M. Blum, Towards a mathematical theory of inductive inference, Inform. and Control 28 (1975), 125-155.
6. J. Case, S. Jain, and A. Sharma, On learning limiting programs, Internat. J. Found. Comput. Sci. 3 (1992), 93-115.
7. J. Case and C. Smith, Comparison of identification criteria for machine inductive inference, Theoret. Comput. Sci. 25 (1983), 193-220.
8. P. Cholak, R. Downey, L. Fortnow, W. Gasarch, E. Kinber, M. Kummer, S. Kurtz, and T. Slaman, Degrees of inferability, in "Proceedings, Fifth Annual ACM Workshop on Computational Learning Theory," pp. 180-192, ACM Press, New York, 1992.
9. R. Epstein, R. Haas, and R. Kramer, Hierarchies of sets and degrees below 0′, in "Logic Year 1979-80," Lecture Notes in Math., Vol. 859, pp. 32-48, Springer-Verlag, Berlin, 1981.
10. L. Fortnow, W. Gasarch, S. Jain, E. Kinber, M. Kummer, S. Kurtz, M. Pleszkoch, T. Slaman, R. Solovay, and F. Stephan, Extremes in the degrees in inferability, Ann. Pure Appl. Logic 66 (1994), 231-276.
11. W. Gasarch and M. Pleszkoch, Learning via queries to an oracle, in "Second Annual Conference on Computational Learning Theory," pp. 214-229, Morgan Kaufmann, San Mateo, CA, 1989.
12. W. Gasarch and C. Smith, Learning via queries, Assoc. Comput. Mach. 39 (1992), 649-675.
13. E. Gold, Language identification in the limit, Inform. and Control 10 (1967), 447-474.
14. C. Haught, The degrees below a 1-generic degree <0′, J. Symbolic Logic 51 (1986), 770-777.
15. S. Jain and A. Sharma, On the non-existence of maximal inference degrees for language identification, Inform. Process. Lett. 47 (1993), 81-88.
16. C. Jockusch, Jr., Degrees of generic sets, in "Recursion Theory: Its Generalizations and Applications," pp. 110-139, Cambridge Univ. Press, Cambridge, 1980.
17. E. Kinber, Some problems of learning with an oracle, in "Third Annual Conference on computational Learning Theory," pp. 178-186, Morgan Kaufmann, San Mateo, CA, 1990.
18. M. Kumabe, A 1-generic degree which bounds a minimal degree, J. Symbolic Logic 55 (1990), 733-743.
19. M. Kummer and F. Stephan, Recursion theoretic properties of frequency computation and bounded queries, Inform. and Comput. 120 (1995), 59-77.
20. M. Lerman, "Degrees of Unsolvability," Springer-Verlag, Berlin, 1983.
21. D. Osherson, M. Stob, and S. Weinstein, "Systems That Learn," MIT Press, Cambridge, MA, 1986.
22. L. Pitt and C. Smith, Probability and plurality for aggregations of learning machines, Inform. and Comput. 11 (1988), 77-92.
23. D. Posner and R. Robinson, Degrees joining to 0′, J. Symbolic Logic 46 (1981), 714-722.
24. T. Slaman and R. Solovay, When oracles do not help, in "Fourth Annual Conference on Computational Learning Theory," pp. 379-383, Morgan Kaufmann, San Mateo, CA, 1991.
25. T. Slaman and J. Steel, Complementation in the Turing degrees, J. Symbolic Logic 54 (1989), 160-176.
26. C. Smith, The power of pluralism for automatic program synthesis, J. Assoc. Comput. Mach. 29 (1982), 1144-1165.
27. R. Soare, "Recursively Enumerable Sets and Degrees," Springer-Verlag, Berlin, 1987.