Completeness and Reduction in Algebraic Complexity Theory

Language: English

Published by Springer, 2010

3642086047 / 9783642086045

Series: Book 3 of 24 - Algorithms and Computation in Mathematics

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Druck auf Anfrage Neuware - Printed after ordering - One of the most important and successful theories in computational complex ity is that of NP-completeness. This discrete theory is based on the Turing machine model and achieves a classification of discrete computational prob lems according to their algorithmic difficulty. Turing machines formalize al gorithms which operate on finite strings of symbols over a finite alphabet. By contrast, in algebraic models of computation, the basic computational step is an arithmetic operation (or comparison) of elements of a fixed field, for in stance of real numbers. Hereby one assumes exact arithmetic. In 1989, Blum, Shub, and Smale [12] combined existing algebraic models of computation with the concept of uniformity and developed a theory of NP-completeness over the reals (BSS-model). Their paper created a renewed interest in the field of algebraic complexity and initiated new research directions. The ultimate goal of the BSS-model (and its future extensions) is to unite classical dis crete complexity theory with numerical analysis and thus to provide a deeper foundation of scientific computation (cf. [11, 101]). Already ten years before the BSS-paper, Valiant [107, 110] had proposed an analogue of the theory of NP-completeness in an entirely algebraic frame work, in connection with his famous hardness result for the permanent [108]. While the part of his theory based on the Turing approach (#P-completeness) is now standard and well-known among the theoretical computer science com munity, his algebraic completeness result for the permanents received much less attention.…

Seller Inventory # 9783642086045

Title
Completeness and Reduction in Algebraic Complexity Theory
Author
Peter Bürgisser
Publisher
Springer
Publication year
2010
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642086047
ISBN 13
9783642086045
Item weight
289 grams
Dimensions
234x156x11 mm
Series
Book 3 of 24: Algorithms and Computation in Mathematics

AHA-BUCH GmbH

Einbeck, Germany

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