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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Bounded Queries in Recursion Theory
• Author: William Levine, Georgia Martin
• Language: English
• Binding: Paperback
• Number of pages: 353
• EAN: 9781461268482
• ISBN: 1461268486
• ID: 02253490
• Publisher: Springer-Verlag New York Inc.
• Weight: 569 g
• Dimensions: 235 × 155 × 21 mm
• Date of publishing: 13. July 2013

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