| Dewey Class |
004.0151 |
| Title |
Bounded Queries in Recursion Theory ([EBook] /) / by William I. Gasarch, Georgia A. Martin. |
| Author |
Gasarch, William I. |
| Added Personal Name |
Martin, Georgia A. author. |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 1999. |
| Physical Details |
XIII, 353 p. : online resource. |
| Series |
Progress in computer science and applied logic ; 16 |
| ISBN |
9781461206354 |
| Summary Note |
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.: |
| Contents note |
A: Getting Your Feet Wet -- 1 Basic Concepts -- 2 Bounded Queries and the Halting Set -- 3 Definitions and Questions -- B: The Complexity of Functions -- 4 The Complexity of CnA -- 5 #nA and Other Functions -- C: The Complexity of Sets -- 6 The Complexity of ODDnA and MODmnA -- 7 Q Versus QC -- 8 Separating and Collapsing Classes -- D: Miscellaneous -- 9 Nondeterministic Complexity -- 10 The Literature on Bounded Queries -- References. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-1-4612-0635-4 |
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