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Titlebook: Bounded Queries in Recursion Theory; William I. Gasarch,Georgia A. Martin Book 1999 Springer Science+Business Media New York 1999 Computab

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发表于 2025-3-21 18:40:05 | 显示全部楼层 |阅读模式
期刊全称Bounded Queries in Recursion Theory
影响因子2023William I. Gasarch,Georgia A. Martin
视频video
学科分类Progress in Computer Science and Applied Logic
图书封面Titlebook: Bounded Queries in Recursion Theory;  William I. Gasarch,Georgia A. Martin Book 1999 Springer Science+Business Media New York 1999 Computab
影响因子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.
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发表于 2025-3-21 22:15:37 | 显示全部楼层
The Complexity of C, the least . such that there exists a set . for which C. ∈ FQ(.,.), but also the number of queries to . . that are required to compute C.. (Note that, numerically speaking, the former complexity cannot exceed the latter.)
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Q Versus QC are studying sets . such that (∃. ≥ l )[Q(., .) QC(., .)]. This condition holds of a set . iff there is some . ≥ 1 with the property that, for every set . ∈ Q(., .): there is an oracle Turing machine M. for deciding . with . queries to . such that, for all .,., the .(.) computation converges after
发表于 2025-3-22 04:36:13 | 显示全部楼层
The Literature on Bounded Queriesajor results found in each. All references in this chapter to numbered theorems, definitions, etc. apply to items in this book, not to items in the individual papers. The papers covered in this bibliography are arranged in alphabetical order by authors’ names
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2297-0576 spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.978-1-4612-6848-2978-1-4612-0635-4Series ISSN 2297-0576 Series E-ISSN 2297-0584
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Book 1999fficulty 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. W
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ome basics from recursion theory. In Section 1.3 we present some concepts from recursion theory that are standard tools of the trade for recursion theorists but may seem a bit more advanced to beginners. In Section 1.4 we present several specialized concepts and results from recursion theory that are later applied to the study of bounded queries.
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