Article

Search Techniques for Rational Polynomial Orders

Authors:

Rafael Navarro-Marset,

Salvador Lucas,

Peter Schneider-KampAuthors Info & Claims

Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics

Pages 109 - 124

https://doi.org/10.1007/978-3-540-85110-3_10

Published: 28 July 2008 Publication History

Abstract

Polynomial interpretations are a standard technique used in almost all tools for proving termination of term rewrite systems (TRSs) automatically. Traditionally, one applies interpretations with polynomials over the naturals. But recently, it was shown that interpretations with polynomials over the rationals can be significantly more powerful. However, searching for such interpretations is considerably more difficult than for natural polynomials. Moreover, while there exist highly efficient SAT-based techniques for finding natural polynomials, no such techniques had been developed for rational polynomials yet. In this paper, we tackle the two main problems when applying rational polynomial interpretations in practice: (1) We develop new criteria to decide when to use rational instead of natural polynomial interpretations. (2) Afterwards, we present SAT-based methods for finding rational polynomial interpretations and evaluate them empirically.

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Cited By

Giesl JAschermann CBrockschmidt MEmmes FFrohn FFuhs CHensel JOtto CPlücker MSchneider-Kamp PStröder TSwiderski SThiemann R(2017)Analyzing Program Termination and Complexity Automatically with AProVEJournal of Automated Reasoning10.1007/s10817-016-9388-y58:1(3-31)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10817-016-9388-y
Zankl HMiddeldorp A(2010)Satisfiability of non-linear (Ir)rational arithmeticProceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning10.5555/1939141.1939168(481-500)Online publication date: 25-Apr-2010
https://dl.acm.org/doi/10.5555/1939141.1939168
Lucas S(2010)From matrix interpretations over the rationals to matrix interpretations over the naturalsProceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics10.5555/1894483.1894495(116-131)Online publication date: 5-Jul-2010
https://dl.acm.org/doi/10.5555/1894483.1894495
Show More Cited By

Search Techniques for Rational Polynomial Orders
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image Guide Proceedings

Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics

July 2008

598 pages

ISBN:9783540851097

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 28 July 2008

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Cited By

Giesl JAschermann CBrockschmidt MEmmes FFrohn FFuhs CHensel JOtto CPlücker MSchneider-Kamp PStröder TSwiderski SThiemann R(2017)Analyzing Program Termination and Complexity Automatically with AProVEJournal of Automated Reasoning10.1007/s10817-016-9388-y58:1(3-31)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1007/s10817-016-9388-y
Zankl HMiddeldorp A(2010)Satisfiability of non-linear (Ir)rational arithmeticProceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning10.5555/1939141.1939168(481-500)Online publication date: 25-Apr-2010
https://dl.acm.org/doi/10.5555/1939141.1939168
Lucas S(2010)From matrix interpretations over the rationals to matrix interpretations over the naturalsProceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics10.5555/1894483.1894495(116-131)Online publication date: 5-Jul-2010
https://dl.acm.org/doi/10.5555/1894483.1894495
Zankl HHirokawa NMiddeldorp A(2009)KBO OrientabilityJournal of Automated Reasoning10.1007/s10817-009-9131-z43:2(173-201)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1007/s10817-009-9131-z
Zankl HMiddeldorp A(2009)Increasing interpretationsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-009-9144-756:1(87-108)Online publication date: 1-May-2009
https://dl.acm.org/doi/10.1007/s10472-009-9144-7

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