Completeness and Reduction in Algebraic Complexity Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000
|
| Schriftenreihe: | Algorithms and Computation in Mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XII, 168 p) |
| ISBN: | 9783662041796 9783642086045 |
| ISSN: | 1431-1550 |
| DOI: | 10.1007/978-3-662-04179-6 |
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| 500 | |a 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 | ||
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Datensatz im Suchindex
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| spelling | Bürgisser, Peter Verfasser aut Completeness and Reduction in Algebraic Complexity Theory by Peter Bürgisser Berlin, Heidelberg Springer Berlin Heidelberg 2000 1 Online-Ressource (XII, 168 p) txt rdacontent c rdamedia cr rdacarrier Algorithms and Computation in Mathematics 7 1431-1550 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 Mathematics Information theory Algebra Computer science / Mathematics Computational Mathematics and Numerical Analysis Theory of Computation Informatik Mathematik Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Algebra (DE-588)4001156-2 s Komplexitätstheorie (DE-588)4120591-1 s 2\p DE-604 Berechnungskomplexität (DE-588)4134751-1 s 3\p DE-604 https://doi.org/10.1007/978-3-662-04179-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bürgisser, Peter Completeness and Reduction in Algebraic Complexity Theory Mathematics Information theory Algebra Computer science / Mathematics Computational Mathematics and Numerical Analysis Theory of Computation Informatik Mathematik Komplexitätstheorie (DE-588)4120591-1 gnd Algebra (DE-588)4001156-2 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4001156-2 (DE-588)4134751-1 (DE-588)4113937-9 |
| title | Completeness and Reduction in Algebraic Complexity Theory |
| title_auth | Completeness and Reduction in Algebraic Complexity Theory |
| title_exact_search | Completeness and Reduction in Algebraic Complexity Theory |
| title_full | Completeness and Reduction in Algebraic Complexity Theory by Peter Bürgisser |
| title_fullStr | Completeness and Reduction in Algebraic Complexity Theory by Peter Bürgisser |
| title_full_unstemmed | Completeness and Reduction in Algebraic Complexity Theory by Peter Bürgisser |
| title_short | Completeness and Reduction in Algebraic Complexity Theory |
| title_sort | completeness and reduction in algebraic complexity theory |
| topic | Mathematics Information theory Algebra Computer science / Mathematics Computational Mathematics and Numerical Analysis Theory of Computation Informatik Mathematik Komplexitätstheorie (DE-588)4120591-1 gnd Algebra (DE-588)4001156-2 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Mathematics Information theory Algebra Computer science / Mathematics Computational Mathematics and Numerical Analysis Theory of Computation Informatik Mathematik Komplexitätstheorie Berechnungskomplexität Hochschulschrift |
| url | https://doi.org/10.1007/978-3-662-04179-6 |
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