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Volumn 39, Issue 3, 2005, Pages 547-586

Polynomials over the reals in proofs of termination: From theory to practice

Author keywords

Algebraic interpretations; Polynomial orderings; Rewriting; Termination

Indexed keywords

ALGEBRA; PROBLEM SOLVING; SYNTACTICS;

EID: 22944474618     PISSN: 09883754     EISSN: 28047346     Source Type: Journal    
DOI: 10.1051/ita:2005029     Document Type: Conference Paper
Times cited : (41)

References (44)
  • 1
    • 0001193616 scopus 로고    scopus 로고
    • Termination of term rewriting using dependency pairs
    • T. Arts and J. Giesl, Termination of Term Rewriting Using Dependency Pairs. Theor. Comput. Sci. 236 (2000) 133-178.
    • (2000) Theor. Comput. Sci. , vol.236 , pp. 133-178
    • Arts, T.1    Giesl, J.2
  • 4
    • 84948973958 scopus 로고    scopus 로고
    • Recursive path orderings can be context-sensitive
    • Proc. of 18th International Conference on Automated Deduction, CADE'02, edited by A. Voronkov, Springer-Verlag, Berlin
    • C. Borralleras, S. Lucas and A. Rubio, Recursive Path Orderings can be Context-Sensitive, in Proc. of 18th International Conference on Automated Deduction, CADE'02, edited by A. Voronkov, Springer-Verlag, Berlin. LNAI 2392 (2002) 314-331.
    • (2002) LNAI , vol.2392 , pp. 314-331
    • Borralleras, C.1    Lucas, S.2    Rubio, A.3
  • 6
    • 0023437488 scopus 로고
    • Termination of rewriting systems by polynomial interpretations and its implementation
    • A. ben Cherifa and P. Lescanne, Termination of rewriting systems by polynomial interpretations and its implementation. Sci. Comput. Program. 9 (1987) 137-160.
    • (1987) Sci. Comput. Program , vol.9 , pp. 137-160
    • Ben Cherifa, A.1    Lescanne, P.2
  • 7
    • 77949586592 scopus 로고
    • Polynomial interpretations and the complexity of algorithms
    • edited by D. Kapur, Springer-Verlag, Berlin. LNAI
    • A. Cichon and P. Lescanne, Polynomial interpretations and the complexity of algorithms, in Proc. of 11th International Conference on Automated Deduction, CADE'92, edited by D. Kapur, Springer-Verlag, Berlin. LNAI 607 (1992) 139-147.
    • (1992) Proc. of 11th International Conference on Automated Deduction, CADE'92 , vol.607 , pp. 139-147
    • Cichon, A.1    Lescanne, P.2
  • 8
    • 3042639683 scopus 로고    scopus 로고
    • Proving termination of rewriting with CiME
    • edited by A. Rubio, Technical Report DSIC 11/15/03, Valencia, Spain
    • E. Contejean and C. Marché, B. Monate and X. Urbain, Proving termination of rewriting with CiME, in Proc. of 6th International Workshop on Termination, WST'03, edited by A. Rubio, Technical Report DSIC 11/15/03, Valencia, Spain (2003) 71-73. Available at http://cime.lri.fr
    • (2003) Proc. of 6th International Workshop on Termination, WST'03 , pp. 71-73
    • Contejean, E.1    Marché, C.2    Monate, B.3    Urbain, X.4
  • 10
    • 0026917938 scopus 로고
    • Simulation of turing machines by a regular rewrite rule
    • M. Dauchet, Simulation of turing machines by a regular rewrite rule. Theor. Comput. Sci. 103 (1992) 409-420.
    • (1992) Theor. Comput. Sci. , vol.103 , pp. 409-420
    • Dauchet, M.1
  • 11
    • 0000386539 scopus 로고
    • A note on simplification orderings
    • N. Dershowitz, A note on simplification orderings. Inform. Proc. Lett. 9 (1979) 212-215.
    • (1979) Inform. Proc. Lett. , vol.9 , pp. 212-215
    • Dershowitz, N.1
  • 12
    • 0001138255 scopus 로고
    • Orderings for term rewriting systems
    • N. Dershowitz, Orderings for term rewriting systems. Theor. Comput. Sci. 17 (1982) 279-301.
    • (1982) Theor. Comput. Sci. , vol.17 , pp. 279-301
    • Dershowitz, N.1
  • 13
    • 84910829499 scopus 로고
    • Termination of rewriting
    • N. Dershowitz, Termination of rewriting. J. Symbol. Comput. 3 (1987) 69-115.
    • (1987) J. Symbol. Comput. , vol.3 , pp. 69-115
    • Dershowitz, N.1
  • 15
    • 10444249658 scopus 로고    scopus 로고
    • Relaxing monotonicity for innermost termination
    • M.-L. Fernández, Relaxing monotonicity for innermost termination. Inform. Proc. Lett. 98 (2005) 117-123.
    • (2005) Inform. Proc. Lett. , vol.98 , pp. 117-123
    • Fernández, M.-L.1
  • 16
    • 0036657874 scopus 로고    scopus 로고
    • Modular termination proofs for rewriting using dependency pairs
    • J. Giesl, T. Arts and E. Ohlebusch, Modular Termination Proofs for Rewriting Using Dependency Pairs. J. Symbol. Comput. 38 (2002) 21-58.
    • (2002) J. Symbol. Comput. , vol.38 , pp. 21-58
    • Giesl, J.1    Arts, T.2    Ohlebusch, E.3
  • 17
    • 0004038821 scopus 로고
    • Ph.D. Thesis. Fakultät für Mathematik und Informatik. Universität Passau
    • A. Geser, Relative Termination. Ph.D. Thesis. Fakultät für Mathematik und Informatik. Universität Passau (1990).
    • (1990) Relative Termination
    • Geser, A.1
  • 18
    • 84955582635 scopus 로고
    • Generating polynomial orderings for termination proofs
    • Proc. of 6th International Conference on Rewriting Techniques and Applications, RTA '95, edited by J. Hsiang, Springer-Verlag, Berlin
    • J. Giesl, Generating Polynomial Orderings for Termination Proofs, in Proc. of 6th International Conference on Rewriting Techniques and Applications, RTA '95, edited by J. Hsiang, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 914 (1995) 426-431.
    • (1995) Lect. Notes Comput. Sci. , vol.914 , pp. 426-431
    • Giesl, J.1
  • 20
    • 3042804926 scopus 로고    scopus 로고
    • Transformation techniques for context-sensitive rewrite systems
    • J. Giesl and A. Middeldorp, Transformation Techniques for Context-Sensitive Rewrite Systems. J. Funct. Program. 14 (2004) 379-427.
    • (2004) J. Funct. Program , vol.14 , pp. 379-427
    • Giesl, J.1    Middeldorp, A.2
  • 21
    • 35048887144 scopus 로고    scopus 로고
    • Automated termination proofs with AProVE
    • Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA'04, edited by V. van Oostrom, Springer-Verlag, Berlin
    • J. Giesl, R. Thiemann, P. Schneider-Kamp and S. Falke, Automated Termination Proofs with AProVE, in Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA'04, edited by V. van Oostrom, Springer-Verlag, Berlin. Lect. Notes. Comput. Sci. 3091 (2004) 210-220. Available at http://www-12.Informatik.rwth-aachen.de/AProVE
    • (2004) Lect. Notes. Comput. Sci. , vol.3091 , pp. 210-220
    • Giesl, J.1    Thiemann, R.2    Schneider-Kamp, P.3    Falke, S.4
  • 22
    • 0032143325 scopus 로고    scopus 로고
    • Testing positiveness of polynomials
    • H. Hong and D. Jakus, Testing Positiveness of Polynomials. J. Automated Reasoning 21 (1998) 23-38.
    • (1998) J. Automated Reasoning , vol.21 , pp. 23-38
    • Hong, H.1    Jakus, D.2
  • 23
    • 84974745030 scopus 로고
    • Termination proofs and the length of derivations
    • Proc. of the 3rd International Conference on Rewriting Techniques and Applications, RTA '89, edited by N. Dershowitz, Springer-Verlag, Berlin
    • D. Hofbauer and C. Lautemann, Termination proofs and the length of derivations, in Proc. of the 3rd International Conference on Rewriting Techniques and Applications, RTA '89, edited by N. Dershowitz, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 355 (1989) 167-177.
    • (1989) Lect. Notes Comput. Sci. , vol.355 , pp. 167-177
    • Hofbauer, D.1    Lautemann, C.2
  • 24
    • 35048819118 scopus 로고    scopus 로고
    • Dependency pairs revisited
    • Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA '04, edited by V. van Oostrom, Springer-Verlag, Berlin
    • N. Hirokawa and A. Middeldorp, Dependency Pairs Revisited, in Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA '04, edited by V. van Oostrom, Springer-Verlag, Berlin. Lect. Notes. Comput. Sci. 3091 (2004) 249-268.
    • (2004) Lect. Notes. Comput. Sci. , vol.3091 , pp. 249-268
    • Hirokawa, N.1    Middeldorp, A.2
  • 25
    • 35048902099 scopus 로고    scopus 로고
    • Polynomial interpretations with negative coefficients
    • Proc. of the 7th International Conference on Artificial Intelligence and Symbolic Computation, AISC'04, edited by B. Buchberger and J.A. Campbell, Springer-Verlag, Berlin
    • N. Hirokawa and A. Middeldorp, Polynomial Interpretations with Negative Coefficients, in Proc. of the 7th International Conference on Artificial Intelligence and Symbolic Computation, AISC'04, edited by B. Buchberger and J.A. Campbell, Springer-Verlag, Berlin. LNAI 3249 (2004) 185-198.
    • (2004) LNAI , vol.3249 , pp. 185-198
    • Hirokawa, N.1    Middeldorp, A.2
  • 26
    • 22944445114 scopus 로고    scopus 로고
    • Tyrolean termination tool
    • Proc. of 16th International Conference on Rewriting Techniques and Applications, RTA'05, edited by J. Giesl., to appear
    • N. Hirokawa and A. Middeldorp, Tyrolean Termination Tool, in Proc. of 16th International Conference on Rewriting Techniques and Applications, RTA'05, edited by J. Giesl. Lect. Notes. Comput. Sci., to appear (2005). Available at http://c12-informatik.uibk.ac.at
    • (2005) Lect. Notes. Comput. Sci.
    • Hirokawa, N.1    Middeldorp, A.2
  • 27
    • 84888234955 scopus 로고    scopus 로고
    • Termination proofs by context-dependent interpretations
    • Proc. of 12th International Conference on Rewriting Techniques and Applications, RTA'01, edited by A. Middeldorp, Springer-Verlag, Berlin
    • D. Hofbauer, Termination Proofs by Context-Dependent Interpretations, in Proc. of 12th International Conference on Rewriting Techniques and Applications, RTA'01, edited by A. Middeldorp, Springer-Verlag, Berlin, Lect. Notes Comput. Sci. 2051 (2001) 108-121.
    • (2001) Lect. Notes Comput. Sci. , vol.2051 , pp. 108-121
    • Hofbauer, D.1
  • 28
    • 0002896422 scopus 로고
    • Simple word problems in universal algebra
    • edited by J. Leech, Pergamon Press
    • D.E. Knuth and P.E. Bendix, Simple Word Problems in Universal Algebra, in Computational Problems in Abstract Algebra, edited by J. Leech, Pergamon Press (1970) 263-297.
    • (1970) Computational Problems in Abstract Algebra , pp. 263-297
    • Knuth, D.E.1    Bendix, P.E.2
  • 29
    • 84979025426 scopus 로고    scopus 로고
    • Argument Filtering Transformation
    • International Conference on Principles and Practice of Declarative Programming, PPDP'99, edited by G. Nadathur, Springer-Verlag, Berlin
    • K. Kusakari, M. Nakamura and Y. Toyama, Argument Filtering Transformation, in International Conference on Principles and Practice of Declarative Programming, PPDP'99, edited by G. Nadathur, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 1702 (1999) 47-61.
    • (1999) Lect. Notes Comput. Sci. , vol.1702 , pp. 47-61
    • Kusakari, K.1    Nakamura, M.2    Toyama, Y.3
  • 31
    • 0012783530 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • S. Lang, Algebra. Springer-Verlag, Berlin (2004).
    • (2004) Algebra
    • Lang, S.1
  • 32
    • 0003006419 scopus 로고    scopus 로고
    • Context-sensitive computations in functional and functional logic programs
    • S. Lucas, Context-sensitive computations in functional and functional logic programs. J. Funct. Logic Program. 1998 (1998) 1-61.
    • (1998) J. Funct. Logic Program , vol.1998 , pp. 1-61
    • Lucas, S.1
  • 33
    • 0037057838 scopus 로고    scopus 로고
    • Context-sensitive rewriting strategies
    • S. Lucas, Context-Sensitive Rewriting Strategies. Inform. Comput. 178 (2002) 293-343.
    • (2002) Inform. Comput. , vol.178 , pp. 293-343
    • Lucas, S.1
  • 34
    • 35248819048 scopus 로고    scopus 로고
    • Termination of (canonical) context-sensitive rewriting
    • Proc. 13th International Conference on Rewriting Techniques and Applications, RTA '02, edited by S. Tison, Springer-Verlag, Berlin
    • S. Lucas, Termination of (Canonical) Context-Sensitive Rewriting, in Proc. 13th International Conference on Rewriting Techniques and Applications, RTA '02, edited by S. Tison, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 2378 (2002) 296-310.
    • (2002) Lect. Notes Comput. Sci. , vol.2378 , pp. 296-310
    • Lucas, S.1
  • 35
    • 35048832942 scopus 로고    scopus 로고
    • MU-TERM: A tool for proving termination of context-sensitive rewriting
    • Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA'04, edited by V. van Oostrom, Springer-Verlag, Berlin
    • S. Lucas, MU-TERM: A Tool for Proving Termination of Context-Sensitive Rewriting, in Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA'04, edited by V. van Oostrom, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 3091 (2004) 200-209. Available at http://www.daic.upv.es/ slucae/car/termination/muterm
    • (2004) Lect. Notes Comput. Sci. , vol.3091 , pp. 200-209
    • Lucas, S.1
  • 38
    • 22944455121 scopus 로고    scopus 로고
    • INRA, France
    • J.P. Rellier, CON'FLEX. INRA, France, 1996. Main URL:http://www.inra.fr/ bia/T/rellier/Logiciels/conflex/welcome.html
    • (1996) CON'FLEX
    • Rellier, J.P.1
  • 39
    • 0028320191 scopus 로고
    • Generating polynomial orderings
    • J. Steinbach, Generating Polynomial Orderings. Inform. Proc. Lett. 49 (1994) 85-93.
    • (1994) Inform. Proc. Lett. , vol.49 , pp. 85-93
    • Steinbach, J.1
  • 40
    • 0029369584 scopus 로고
    • Simplification orderings: History of results
    • J. Steinbach, Simplification orderings: History of results. Fundamenta, Informaticae 24 (1995) 47-88.
    • (1995) Fundamenta, Informaticae , vol.24 , pp. 47-88
    • Steinbach, J.1
  • 42
    • 9444229424 scopus 로고    scopus 로고
    • Improved modular termination proofs using dependency pairs
    • Proc. of 2nd International Joint Conference on Automated Reasoning, IJCAR'04, edited by D.A. Basin and M. Rusinowitch, Springer-Verlag, Berlin
    • R. Thiemann, J. Giesl and P. Schneider-Kamp, Improved Modular Termination Proofs Using Dependency Pairs, in Proc. of 2nd International Joint Conference on Automated Reasoning, IJCAR'04, edited by D.A. Basin and M. Rusinowitch, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 3097 (2004) 75-90.
    • (2004) Lect. Notes Comput. Sci. , vol.3097 , pp. 75-90
    • Thiemann, R.1    Giesl, J.2    Schneider-Kamp, P.3
  • 43
    • 84947711132 scopus 로고    scopus 로고
    • Termination of context-sensitive rewriting
    • Proc. of 8th International Conference on Rewriting Techniques and Applications, RTA '97, edited by H. Comon, Springer-Verlag, Berlin
    • H. Zantema, Termination of Context-Sensitive Rewriting, in Proc. of 8th International Conference on Rewriting Techniques and Applications, RTA '97, edited by H. Comon, Springer-Verlag, Berlin. Lect. Notes Comput. Sci. 1232 (1997) 172-186.
    • (1997) Lect. Notes Comput. Sci. , vol.1232 , pp. 172-186
    • Zantema, H.1
  • 44
    • 18944374600 scopus 로고    scopus 로고
    • Termination
    • Chap. 6. edited by TeReSe, Cambridge University Press
    • H. Zantema, Termination, in Term Rewriting Systems, Chap. 6. edited by TeReSe, Cambridge University Press (2003).
    • (2003) Term Rewriting Systems
    • Zantema, H.1


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