Abstract
Most systems for the automation of termination proofs using polynomial orderings are only semi-automatic, i.e. the “right” polynomial ordering has to be given by the user. We show that a variation of Lank-ford's partial derivative technique leads to an easier and slightly more powerful method than most other semi-automatic approaches. Based on this technique we develop a method for the automated synthesis of a suited polynomial ordering.
Preview
Unable to display preview. Download preview PDF.
References
F. Bellegarde. Rewriting Systems on FP Expressions that reduce the Number of Sequences they yield. Symp. LISP & Funct. Prog., ACM, Austin, TX, 1984.
A. Ben Cherifa & P. Lescanne. Termination of Rewriting Systems by Polynomial Interpretations and its Implementation. Science of Computer Programming, 9(2):137–159, 1987.
G. E. Collins. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In Proc. 2nd GI Conf. on Automata Theory and Formal Languages, Kaiserslautern, Germany, 1975.
N. Dershowitz. Orderings for Term-Rewriting Systems. Theoretical Computer Science, 17:279–301, 1982.
N. Dershowitz. Termination of Rewriting. Journal of Symbolic Computation, 3(1, 2):69–115, 1987.
N. Dershowitz & J.-P. Joannaud. Rewrite Systems. Handbook of Theoretical Comp. Science, J. van Leuwen, Ed., vol. B, ch. 6, 243–320, Elsevier, 1990.
G. Huet & D. S. Lankford. On the Uniform Halting Problem for Term Rewriting Systems. Rapport Laboria 283, Institut de Recherche d'Informatique et d'Automatique, Le Chesnay, France, 1978.
D. S. Lankford. A Finite Termination Algorithm. Internal Memo, Southwestern University, Georgetown, TX, 1976.
D. S. Lankford. On Proving Term Rewriting Systems are Noetherian. Technical Report Memo MTP-3, Louisiana Tech. Univ., Ruston, LA, 1979.
J. Steinbach. Termination Proofs of Rewriting Systems — Heuristics for Generating Polynomial Orderings. SEKI-Report SR-91-14, Univ. Kaiserslautern, Germany, 1991.
J. Steinbach. Proving Polynomials Positive. In Proc. 12th Conf. Foundations Software Technology & Theoretical Comp. Sc., New Delhi, India, 1992.
A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley, 1951.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giesl, J. (1995). Generating polynomial orderings for termination proofs. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_77
Download citation
DOI: https://doi.org/10.1007/3-540-59200-8_77
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59200-6
Online ISBN: 978-3-540-49223-8
eBook Packages: Springer Book Archive