E-Book, Englisch, Band 16, 353 Seiten, eBook
Levine / Martin Bounded Queries in Recursion Theory
Erscheinungsjahr 2012
ISBN: 978-1-4612-0635-4
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 16, 353 Seiten, eBook
Reihe: Progress in Computer Science and Applied Logic
ISBN: 978-1-4612-0635-4
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
