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Complexity Theory of Real Functions (Progress in Theoretical Computer Science), by Ker-I Ko
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Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.
- Sales Rank: #6573748 in Books
- Brand: Brand: Birkhäuser Boston
- Published on: 1991-10-01
- Original language: English
- Number of items: 1
- Dimensions: 9.75" h x 6.50" w x .75" l, .0 pounds
- Binding: Hardcover
- 310 pages
- Used Book in Good Condition
Most helpful customer reviews
7 of 7 people found the following review helpful.
This is an important book in complexity theory.
By A Customer
This is an important book in complexity theory. It ties the discrete complexity theory of NP-completeness with numerical computation of continuous functions. Traditionally, numerical computation uses floating-point machines as the computational model and the theory is very messy. More recently, there are several approaches trying to create a more coherent theory with discrete complexity theory. This theory using Turing machines as a model is one of them. The advantage of this approach is that it makes a direct connection with the NP-completeness theory. The book is well-written and includes a brief review of discrete complexity theory.
0 of 11 people found the following review helpful.
Bad
By A Customer
I think it was the worst book ever. Don't understand why he wrote it
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