Completeness and Reduction in Algebraic Complexity Theory
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1
Completeness and Reduction in Algebraic Complexity Theory (1989)
~EN NW EB DL
ISBN: 9783662041796 bzw. 3662041790, vermutlich in Englisch, Springer Shop, neu, E-Book, elektronischer Download.
Lieferung aus: Schweiz, Lagernd, zzgl. Versandkosten.
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. eBook.
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. eBook.
2
Completeness and Reduction in Algebraic Complexity Theory (1989)
~EN NW EB DL
ISBN: 9783662041796 bzw. 3662041790, vermutlich in Englisch, Springer Berlin Heidelberg, neu, E-Book, elektronischer Download.
Lieferung aus: Deutschland, Versandkostenfrei.
Completeness and Reduction in Algebraic Complexity Theory: 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. Englisch, Ebook.
Completeness and Reduction in Algebraic Complexity Theory: 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. Englisch, Ebook.
3
Completeness and Reduction in Algebraic Complexity Theory (Algorithms and Computation in Mathematics) (2010)
EN HC NW RP EB DL
ISBN: 9783662041796 bzw. 3662041790, in Englisch, 168 Seiten, Springer, gebundenes Buch, neu, Nachdruck, E-Book, elektronischer Download.
Lieferung aus: Deutschland, E-Book zum Download, Versandkostenfrei.
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., Kindle Edition, Ausgabe: Softcover reprint of hardcover 1st ed. 2000, Format: Kindle eBook, Label: Springer, Springer, Produktgruppe: eBooks, Publiziert: 2010-12-03, Freigegeben: 2000-07-26, Studio: Springer.
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., Kindle Edition, Ausgabe: Softcover reprint of hardcover 1st ed. 2000, Format: Kindle eBook, Label: Springer, Springer, Produktgruppe: eBooks, Publiziert: 2010-12-03, Freigegeben: 2000-07-26, Studio: Springer.
4
Completeness and Reduction in Algebraic Complexity Theory
~EN PB NW
ISBN: 9783662041796 bzw. 3662041790, vermutlich in Englisch, Taschenbuch, neu.
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