Algebraic Complexity Theory: With the Collaboration of Thomas Lickteig
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1997
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
315 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems |
| Beschreibung: | 1 Online-Ressource (XXIII, 618 p) |
| ISBN: | 9783662033388 9783642082283 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-03338-8 |
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Datensatz im Suchindex
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| author | Bürgisser, Peter |
| author_facet | Bürgisser, Peter |
| author_role | aut |
| author_sort | Bürgisser, Peter |
| author_variant | p b pb |
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| bvnumber | BV042423254 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03338-8 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9783662033388 9783642082283 |
| issn | 0072-7830 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Bürgisser, Peter Verfasser aut Algebraic Complexity Theory With the Collaboration of Thomas Lickteig by Peter Bürgisser, Michael Clausen, Mohammad Amin Shokrollahi Berlin, Heidelberg Springer Berlin Heidelberg 1997 1 Online-Ressource (XXIII, 618 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 315 0072-7830 The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems Mathematics Computer software Geometry, algebraic Group theory Matrix theory Algorithms Combinatorics Algorithm Analysis and Problem Complexity Algebraic Geometry Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Mathematik Algebra (DE-588)4001156-2 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Algebra (DE-588)4001156-2 s Komplexitätstheorie (DE-588)4120591-1 s 1\p DE-604 Clausen, Michael Sonstige oth Shokrollahi, Mohammad Amin Sonstige oth https://doi.org/10.1007/978-3-662-03338-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bürgisser, Peter Algebraic Complexity Theory With the Collaboration of Thomas Lickteig Mathematics Computer software Geometry, algebraic Group theory Matrix theory Algorithms Combinatorics Algorithm Analysis and Problem Complexity Algebraic Geometry Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Mathematik Algebra (DE-588)4001156-2 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4120591-1 |
| title | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig |
| title_auth | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig |
| title_exact_search | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig |
| title_full | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig by Peter Bürgisser, Michael Clausen, Mohammad Amin Shokrollahi |
| title_fullStr | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig by Peter Bürgisser, Michael Clausen, Mohammad Amin Shokrollahi |
| title_full_unstemmed | Algebraic Complexity Theory With the Collaboration of Thomas Lickteig by Peter Bürgisser, Michael Clausen, Mohammad Amin Shokrollahi |
| title_short | Algebraic Complexity Theory |
| title_sort | algebraic complexity theory with the collaboration of thomas lickteig |
| title_sub | With the Collaboration of Thomas Lickteig |
| topic | Mathematics Computer software Geometry, algebraic Group theory Matrix theory Algorithms Combinatorics Algorithm Analysis and Problem Complexity Algebraic Geometry Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Mathematik Algebra (DE-588)4001156-2 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Mathematics Computer software Geometry, algebraic Group theory Matrix theory Algorithms Combinatorics Algorithm Analysis and Problem Complexity Algebraic Geometry Linear and Multilinear Algebras, Matrix Theory Group Theory and Generalizations Mathematik Algebra Komplexitätstheorie |
| url | https://doi.org/10.1007/978-3-662-03338-8 |
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