Detecting all dependences in systems of geometric constraints using the witness method

Dominique Michelucci, Sebti Foufou

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    In geometric constraints solving, the detection of dependences and the decomposition of the system into smaller subsystems are two important steps that characterize any solving process, but nowadays solvers, which are graph-based in most of the cases, fail to detect dependences due to geometric theorems and to decompose such systems. In this paper, we discuss why detecting all dependences between constraints is a hard problem and propose to use the witness method published recently to detect both structural and non structural dependences. We study various examples of constraints systems and show the promising results of the witness method in subtle dependences detection and systems decomposition.

    Original languageEnglish (US)
    Title of host publicationAutomated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers
    Pages98-112
    Number of pages15
    StatePublished - Dec 1 2007
    Event6th International Workshop on Automated Deduction in Geometry, ADG 2006 - Pontevedra, Spain
    Duration: Aug 31 2006Sep 2 2006

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4869 LNAI
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other6th International Workshop on Automated Deduction in Geometry, ADG 2006
    CountrySpain
    CityPontevedra
    Period8/31/069/2/06

    Fingerprint

    Geometric Constraints
    Decomposition
    Decompose
    Geometric Constraint Solving
    Geometric theorem
    Subsystem
    Graph in graph theory

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Michelucci, D., & Foufou, S. (2007). Detecting all dependences in systems of geometric constraints using the witness method. In Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers (pp. 98-112). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4869 LNAI).

    Detecting all dependences in systems of geometric constraints using the witness method. / Michelucci, Dominique; Foufou, Sebti.

    Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. p. 98-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4869 LNAI).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Michelucci, D & Foufou, S 2007, Detecting all dependences in systems of geometric constraints using the witness method. in Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4869 LNAI, pp. 98-112, 6th International Workshop on Automated Deduction in Geometry, ADG 2006, Pontevedra, Spain, 8/31/06.
    Michelucci D, Foufou S. Detecting all dependences in systems of geometric constraints using the witness method. In Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. p. 98-112. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Michelucci, Dominique ; Foufou, Sebti. / Detecting all dependences in systems of geometric constraints using the witness method. Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. pp. 98-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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