论文信息 - Effective Search Problems

Effective Search Problems

The task of computing a function F with the help of an oracle X can be viewed as a search problem where the cost measure is the number of queries to X. We ask for the minimal number that can be achieved by a suitable choice of X and call this quantity the query complexity of F. This concept is suggested by earlier work of Beigel, Gasarch, Gill, and Owings on “Bounded query classes”. We introduce a fault tolerant version and relate it with Ulam's game. For many natural classes of functions F we obtain tight upper and lower bounds on the query complexity of F. Previous results like the Nonspeedup Theorem and the Cardinality Theorem appear in a wider perspective. Mathematics Subject Classification: 03D20, 68Q15, 68R05.

Frank Stephan | Martin Kummer | F. Stephan | M. Kummer

[1] R. Soare,et al. Π⁰₁ classes and degrees of theories , 1972 .

[2] Joel H. Spencer,et al. Coping with Errors in Binary Search Procedures , 1980, J. Comput. Syst. Sci..

[3] R. Soare. Recursively enumerable sets and degrees , 1987 .

[4] P. Odifreddi. Classical recursion theory , 1989 .

[5] William I. Gasarch,et al. On the Complexity of Finding the Chromatic Number of a Recursive Graph I: The Bounded Case , 1989, Ann. Pure Appl. Log..

[6] James C. Owings,et al. A cardinality version of Beigel's nonspeedup theorem , 1989, Journal of Symbolic Logic.

[7] Daniele Mundici. The Complexity of Adaptive Error-Correcting Codes , 1990, CSL.

[8] Richard Beigel. Unbounded Searching Slgorithms , 1990, SIAM J. Comput..

[9] William I. Gasarch,et al. Bounded queries in recursion theory: a survey , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[10] Martin Kummer. A Proof of Beigel's Cardinality Conjecture , 1992, J. Symb. Log..

[11] Valentina S. Harizanov,et al. Frequency Computations and the Cardinality Theorem , 1992, J. Symb. Log..

[12] Joel H. Spencer,et al. Ulam's Searching Game with a Fixed Number of Lies , 1992, Theor. Comput. Sci..

[13] John Gill,et al. Terse, Superterse, and Verbose Sets , 1993, Inf. Comput..

[14] Efim B. Kinber,et al. Frequency Computation and Bounded Queries , 1996, Theor. Comput. Sci..