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Seidl, Andreas

Cylindrical Decomposition Under Application-Oriented Paradigms

Zylindrische Dekomposition unter anwendungsorientierten Paradigmen

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SWD-Schlagwörter:		Quantorenelimination
Freie Schlagwörter (Englisch):		cylindrical algebraic decomposition , CAD , cylindrical subdecomposition , SCAD , quantifier elimination , QE
MSC - Klassifikation:		03C10
Beteiligte Einrichtung:		Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Fakultät:		Fakultät für Informatik und Mathematik
DDC-Sachgruppe:		Mathematik
Dokumentart:		Dissertation
Hauptberichter:		Weispfenning, Volker (Prof. Dr.)
Sprache:		Englisch
Tag der mündlichen Prüfung:		30.11.2006
Erstellungsjahr:		2006
Publikationsdatum:		06.12.2006
Kurzfassung auf Englisch:		Quantifier elimination (QE) is a powerful tool for problem solving. Once a problem is expressed as a formula, such a method converts it to a simpler, quantifier-free equivalent, thus solving the problem. Particularly many problems live in the domain of real numbers, which makes real QE very interesting. Among the so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm that satisfies these standards would concentrate on generic cases and postpone special and degenerated ones to be treated separately or to be abandoned completely. It would give a solution, which is locally correct for a region the user is interested in. It would give answers, which can provide much valuable information in particular for decision problems. It would combine these methods with more specialized ones, for subcases that allow for. It would exploit degrees of freedom in the algorithms by deciding to proceed in a way that promises to be efficient. It is the focus of this dissertation to treat these challenges. Algorithms described here are implemented in the computer logic system REDLOG and ship with the computer algebra system REDUCE.

Hinweis zum Urheberrecht

URN: http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-816
URL dieser Seite: http://www.opus-bayern.de/uni-passau/volltexte/2006/81/