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Bounded Queries in Recursion Theory by William Levine

Bounded Queries in Recursion Theory

by William Levine
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Book cover type: Paperback
  • ISBN13: 9781461268482
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 353
  • Original Price: EUR 99.99
  • Language: English
  • Edition: 1999
  • Item Weight: 561 grams
  • BISAC Subject(s): Data Science / General, Functional Analysis, and Computer Science

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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