Inclusion problems in parallel learning and games

Journal of Computer and System Sciences

Volumn 52, Issue 3, 1996, Pages 403-420

  Kummer, Martin ^a   Stephan, Frank ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GAME THEORY; MATHEMATICAL MODELS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING; RECURSIVE FUNCTIONS; SET THEORY;

LEARNABLE CLASS; PAIRWISE DISTINCT FUNCTIONS; PARALLEL LEARNING; RECURSION THEORY;

LEARNING SYSTEMS;

EID: 0030168525     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1996.0031     Document Type: Article

References (25)

1. R. Beigel, W. Gasarch, J. Gill, and J. Owings, Terse, superterse, and verbose sets, Inform. and Comput. 103 (1993), 68-85.
2. J. Case and C. Smith, Comparison of identification criteria for machine inductive inference, Theoret. Comput. Sci. 25 (1983), 193-220.
3. R. Daley, B. Kalyanasundaram, and M. Velauthapillai, Breaking the probability 1\2 barrier in FIN-type learning, J. Comput. System Sci. 50 (1995), 574-599.
4. A. N. Degtev, Solvability of the ∀∃-theory of a certain factor-lattice of recursively enumerable sets, Algebra and Logic 17 (1978), 94-101.
5. A. N. Degtev, On (m, n)-computable sets, in "Algebraic Systems" (D. I. Moldavanskij, Ed.), pp. 88-99, Ivanova Gos. Univ., 1981. [Russian]
6. 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 of inferability, Ann. Pure Appl. Logic 66 (1994), 231-276.
7. E. M. Gold, Language identification in the limit, Inform. and Control. 10 (1967), 447-474.
8. V. Harizanov, M. Kummer, and J. Owings, Frequency computation and the cardinality theorem, J. Symbolic Logic 57 (1992), 682-687.
9. C. G. Jockusch, Jr., Degrees of functions with no fixed points, in "Logic, Methodology and Philosophy of Science VIII," pp. 191-201, Elsevier, Amsterdam, 1989.
10. E. Kinber, "Frequency Computable Functions and Frequency Enumerable Sets," Candidate Dissertation, Riga, 1975. [Russian]
11. E. Kinber, C. Smith, M. Velauthapillai, and R. Wiehagen, On learning multiple concepts in parallel, J. Comput. System Sci. 50 (1995), 41-52.
12. E. Kinber and R. Wiehagen, Parallel learning - A recursion-theoretic approach, Informatik, Preprint 10, Fachbereich Informatik, Humboldt-Universität, Berlin, 1991.
13. M. Kummer, The strength of noninclusions for teams of finite learners, in "Proceedings, Sixth Annual ACM Conference on Computational Learning Theory, COLT'94," pp. 268-277, ACM Press, New York, 1994.
14. M. Kummer and F. Stephan, "Some Aspects of Frequency Computation," Technical Report 21/91, Fakultät für Informatik, Universität Karlsruhe, 1991.
15. M. Kummer and F. Stephan, On the structure degrees of inferability, J. Comput. System Sci., to appear; extended abstract in "Proceedings Sixth Annual ACM Conference on Computational Learning Theory, COLT'93," pp. 117-126, ACM Press, New York, 1993.
16. M. Kummer and F. Stephan, The power of frequency computation (extended abstract), in "Proceedings, FCT'95," Lecture Notes in Computer Science, Vol. 965, pp. 323-332, Springer-Verlag, Berlin, 1995.
17. A. H. Lachlan, On some games which are relevant to the theory of recursively enumerable sets, Ann. Math. Ser. 2 91 (1970), 291-310.
18. R. McNaughton, Infinite games played on finite graphs, Ann. Pure Appl. Logic 65 (1993), 149-184.
19. T. McNicholl, "The Inclusion Problem for Generalized Frequency Classes," Ph.D. thesis, Dept. of Mathematics, George Washington University, Washington, DC, May 1995.
20. P. Odifreddi, "Classical Recursion Theory," North-Holland, Amsterdam, 1989.
21. D. Osherson, M. Stob, and S. Weinstein, "Systems That Learn," MIT Press, Cambridge, MA, 1986.
22. M. Ott, "Strategien in Aufzählungsspielen," Diplomarbeit, Fakultät für Informatik, Universität Karlsruhe, 1995.
23. G. F. Rose, An extended notion of computability, in "International Congress for Logic, Methodology and Philosophy of Science, Abstracts," p. 12, Stanford, CA, 1960.
24. R. I. Soare, "Recursively Enumerable Sets and Degrees," Springer-Verlag, Berlin, 1987.
25. B. A. Trakhtenbrot, On frequency computation of functions, Algebra i Logika 2 (1963), 25-32. [Russian]