Bounded Queries in Recursion Theory
Author | : William S. Levine |
Publisher | : Springer Science & Business Media |
Total Pages | : 372 |
Release | : 1998-12-23 |
ISBN-10 | : 0817639667 |
ISBN-13 | : 9780817639662 |
Rating | : 4/5 (662 Downloads) |
Download or read book Bounded Queries in Recursion Theory written by William S. Levine and published by Springer Science & Business Media. This book was released on 1998-12-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.