Ebook: Bounded Queries in Recursion Theory
- Tags: Math Applications in Computer Science, Operator Theory, Theory of Computation, Discrete Mathematics in Computer Science, Computational Mathematics and Numerical Analysis, Applications of Mathematics
- Series: Progress in Computer Science and Applied Logic 16
- Year: 1999
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Basic Concepts....Pages 3-42
Bounded Queries and the Halting Set....Pages 43-52
Definitions and Questions....Pages 53-73
Front Matter....Pages 75-75
The Complexity of C n A ....Pages 77-141
# n A and Other Functions....Pages 143-182
Front Matter....Pages 183-183
The Complexity of ODD n A and MODm n A ....Pages 185-216
Q Versus QC....Pages 217-253
Separating and Collapsing Classes....Pages 255-269
Front Matter....Pages 271-271
Nondeterministic Complexity....Pages 273-293
The Literature on Bounded Queries....Pages 295-324
Back Matter....Pages 325-353
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Basic Concepts....Pages 3-42
Bounded Queries and the Halting Set....Pages 43-52
Definitions and Questions....Pages 53-73
Front Matter....Pages 75-75
The Complexity of C n A ....Pages 77-141
# n A and Other Functions....Pages 143-182
Front Matter....Pages 183-183
The Complexity of ODD n A and MODm n A ....Pages 185-216
Q Versus QC....Pages 217-253
Separating and Collapsing Classes....Pages 255-269
Front Matter....Pages 271-271
Nondeterministic Complexity....Pages 273-293
The Literature on Bounded Queries....Pages 295-324
Back Matter....Pages 325-353
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