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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Abnormal

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.)

debris

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

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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

Resection

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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acrobat

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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