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Improved Matrix Interpretation

  • Conference paper
SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5901))

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Abstract

We present a new technique to prove termination of Term Rewriting Systems, with full automation. A crucial task in this context is to find suitable well-founded orderings. A popular approach consists in interpreting terms into a domain equipped with an adequate well-founded ordering. In addition to the usual interpretations: natural numbers or polynomials over integer/rational numbers, the recently introduced matrix based interpretations have proved to be very efficient regarding termination of string rewriting and of term rewriting. In this spirit we propose to interpret terms as polynomials over integer matrices. Designed for term rewriting, our generalisation subsumes previous approaches allowing for more orderings without increasing the search space. Thus it performs better than the original version. Another advantage is that, interpreting terms to actual polynomials of matrices, it opens the way to matrix non linear interpretations. This result is implemented in the CiME3 rewriting toolkit.

Work partially supported by A3PAT project of the French ANR (ANR-05-BLAN-0146-01).

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Authors and Affiliations

  1. Cédric – CNAM, Paris, France

    Pierre Courtieu, Gladys Gbedo & Olivier Pons

Authors
  1. Pierre Courtieu
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  2. Gladys Gbedo
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  3. Olivier Pons
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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Courtieu, P., Gbedo, G., Pons, O. (2010). Improved Matrix Interpretation. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

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