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  Automatic Verification of the Adequacy of Models for Families of Geometric Objects

Lasaruk, A., & Sturm, T. (2011). Automatic Verification of the Adequacy of Models for Families of Geometric Objects. In T. Sturm, & C. Zengler (Eds.), Automated Deduction in Geometry (pp. 116-140). Berlin: Springer. doi:10.1007/978-3-642-21046-4_6.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-0010-14E8-D Versions-Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-1349-0
Genre: Konferenzbeitrag

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Urheber

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 Urheber:
Lasaruk, Aless1, Autor
Sturm, Thomas2, Autor           
Affiliations:
1External Organizations, ou_persistent22              
2Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              

Inhalt

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Schlagwörter: -
 Zusammenfassung: We consider parametric families of semi-algebraic geometric objects, each implicitly defined by a first-order formula. Given an unambiguous description of such an object family and an intended alternative description we automatically construct a first-order formula which is true if and only if our alternative description uniquely describes geometric objects of the reference description. We can decide this formula by applying real quantifier elimination. In the positive case we furthermore derive the defining first-order formulas corresponding to our new description. In the negative case we can produce sample points establishing a counterexample for the uniqueness. We demonstrate our method by automatically proving uniqueness theorems for characterizations of several geometric primitives and simple complex objects. Finally, we focus on tori, characterizations of which can be applied in spline approximation theory with toric segments. Although we cannot yet practically solve the fundamental open questions in this area within reasonable time and space, we demonstrate that they can be formulated in our framework. In addition this points at an interesting and practically relevant challenge problem for automated deduction in geometry in general.

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Sprache(n): eng - English
 Datum: 20112011
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 619018
DOI: 10.1007/978-3-642-21046-4_6
URI: http://www.springerlink.com/content/6n473q44l527qmw7/fulltext.pdf
Anderer: Local-ID: C125716C0050FB51-6C7DAF04032485E3C1257987003DD415-LasarukSturm:11a
 Art des Abschluß: -

Veranstaltung

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Titel: 7th International Workshop on Automated Deduction in Geometry
Veranstaltungsort: Shanghai, China
Start-/Enddatum: 2008-09-22 - 2008-09-24

Entscheidung

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Projektinformation

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Quelle 1

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Titel: Automated Deduction in Geometry
  Untertitel : 7th International Workshop, ADG 2008, Shanghai, China, September 22-24, 2008. Revised Papers
  Kurztitel : ADG 2008
Genre der Quelle: Konferenzband
 Urheber:
Sturm, Thomas1, Herausgeber           
Zengler, Christoph2, Herausgeber
Affiliations:
1 Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545            
2 External Organizations, ou_persistent22            
Ort, Verlag, Ausgabe: Berlin : Springer
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 116 - 140 Identifikator: ISBN: 978-3-642-21045-7

Quelle 2

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Titel: Lecture Notes in Artificial Intelligence
  Kurztitel : LNAI
Genre der Quelle: Reihe
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 6301 Artikelnummer: - Start- / Endseite: - Identifikator: -