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Completeness and Reduction in Algebraic Complexity Theory: 7 - Brossura
Libro 3 di 24: Algorithms and Computation in Mathematics
Sinossi
Bürgisser, a top expert on algebraic complexity theory, has written a monograph on current research in this field. This book gives new results in the theory of NP-completeness. It is written for mathematicians and computer scientists on both research and graduate level.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
".... The subject matter of the book is not easy, since it involves prerequisites from several areas, among them complexity theory, combinatorics, analytic number theory, and representations of symmetric and general linear groups. But the author goes to great lengths to motivate his results, to put them into perspective, and to explain the proofs carefully. In summary, this monograph advances its area of algebraic complexity theory, and is a must for people for working on this subject. And it is a pleasure to read."
Joachim von zur Gathen, Mathematical Reviews, Issue 2001g
Contenuti
1 Introduction.- 2 Valiant’s Algebraic Model of NP-Completeness.- 3 Some Complete Families of Polynomials.- 4 Cook’s versus Valiant’s Hypothesis.- 5 The Structure of Valiant’s Complexity Classes.- 6 Fast Evaluation of Representations of General Linear Groups.- 7 The Complexity of Immanants.- 8 Separation Results and Future Directions.- References.- List of Notation.
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Completeness and Reduction in Algebraic Complexity Theory (eng)
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Completeness and Reduction in Algebraic Complexity Theory
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Completeness and Reduction in Algebraic Complexity Theory
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Springer Berlin Heidelberg Dez 2010, 2010
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ISBN 13: 9783642086045
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants. 184 pp. Englisch. Codice articolo 9783642086045
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Completeness and Reduction in Algebraic Complexity Theory (Algorithms and Computation in Mathematics, 7)
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Completeness and Reduction in Algebraic Complexity Theory
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Only monograph with the latest results in the field.This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant s algebraic theory of NP-completeness inte. Codice articolo 5047641
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Taschenbuch. Condizione: Neu. 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. Codice articolo 9783642086045
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Completeness and Reduction in Algebraic Complexity Theory
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Springer, Springer Vieweg Dez 2010, 2010
ISBN 10: 3642086047
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Bürgisser, a top expert on algebraic complexity theory, has written a monograph on current research in this field. This book gives new results in the theory of NP-completeness. It is written for mathematicians and computer scientists on both research and graduate level.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 184 pp. Englisch. Codice articolo 9783642086045
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