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＜電子ブック＞
Bounded Queries in Recursion Theory / by William Levine, Georgia Martin
(Progress in Computer Science and Applied Logic. ISSN:22970584 ; 16)

版	1st ed. 1999.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	1999
本文言語	英語
大きさ	XIII, 353 p : online resource
著者標目	*Levine, William author Martin, Georgia author SpringerLink (Online service)
件　名	LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Operator theory LCSH:Computer science LCSH:Discrete mathematics LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Mathematics FREE:Mathematical Applications in Computer Science FREE:Operator Theory FREE:Theory of Computation FREE:Discrete Mathematics in Computer Science FREE:Computational Mathematics and Numerical Analysis FREE:Applications of Mathematics
一般注記	A: Getting Your Feet Wet -- 1 Basic Concepts -- 2 Bounded Queries and the Halting Set -- 3 Definitions and Questions -- B: The Complexity of Functions -- 4 The Complexity of CnA -- 5 #nA and Other Functions -- C: The Complexity of Sets -- 6 The Complexity of ODDnA and MODmnA -- 7 Q Versus QC -- 8 Separating and Collapsing Classes -- D: Miscellaneous -- 9 Nondeterministic Complexity -- 10 The Literature on Bounded Queries -- References One of the major concerns of theoretical computer science is the classifi­ cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function HTTP:URL=https://doi.org/10.1007/978-1-4612-0635-4

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