Abstract
The dependency pair method of Arts and Giesl is the most powerful technique for proving termination of term rewrite systems automatically. We show that the method can be improved by using tree automata techniques to obtain better approximations of the dependency graph. This graph determines the ordering constraints that need to be solved in order to conclude termination. We further show that by using our approximations the dependency pair method provides a decision procedure for termination of right-ground rewrite systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Arts. System description: The dependency pair method. In Proc. 11th RTA, volume 1833 of LNCS, pages 261–264, 2000.
T. Arts and J. Giesl. Modularity of termination using dependency pairs. In Proc. 9th RTA, volume 1379 of LNCS, pages 226–240, 1998.
T. Arts and J. Giesl. Applying rewriting techniques to the verification of Erlang processes. In Proc. 13th CSL, volume 1862 of LNCS, pages 457–471, 2000.
T. Arts and J. Giesl. Termination of term rewriting using dependency pairs. The-oretical Computer Science, 236:133–178, 2000.
F. Baader and T. Nipkow. Term Rewriting and All That. Cambridge University Press, 1998.
F. Bellegarde and P. Lescanne. Termination by completion. Applicable Algebra in Engineering, Communication and Computing, 1:79–96, 1990.
H. Comon. Sequentiality, monadic second-order logic and tree automata. Information and Computation, 157:25–51, 2000.
H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications, 1999. Draft, available from http://www.grappa.univ-lille3.fr/tata/.
N. Dershowitz. Termination of linear rewriting systems (preliminary version). In Proc. 8th ICALP, volume 115 of LNCS, pages 448–458, 1981.
N. Dershowitz. Orderings for term-rewriting systems. Theoretical Computer Science, 17:279–301, 1982.
I. Durand and A. Middeldorp. Decidable call by need computations in term rewriting. In Proc. 14th CADE, volume 1249 of LNAI, pages 4–18, 1997.
J. Giesl and T. Arts. Verification of Erlang processes by dependency pairs. Applicable Algebra in Engineering, Communication and Computing, 2001. To appear.
J. Giesl and A. Middeldorp. Eliminating dummy elimination. In Proc. 17th CADE, volume 1831 of LNAI, pages 309–323, 2000.
J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proc. FroCoS’98, volume 7 of Studies in Logic and Computation, pages 141–160. Wiley, 2000.
G. Huet and J.-J. Lévy. Computations in orthogonal rewriting systems, I and II. In Computational Logic, Essays in Honor of Alan Robinson, pages 396–443. The MIT Press, 1991. Original version: Report 359, Inria, 1979.
F. Jacquemard. Decidable approximations of term rewriting systems. In Proc. 7th RTA, volume 1103 of LNCS, pages 362–376, 1996.
S. Kamin and J.J. Lévy. Two generalizations of the recursive path ordering. Unpublished manuscript, University of Illinois, 1980.
D.E. Knuth and P. Bendix. Simple word problems in universal algebras. In Computational Problems in Abstract Algebra, pages 263–297. Pergamon Press, 1970.
K. Kusakari. Termination, AC-Termination and Dependency Pairs of Term Rewriting Systems. PhD thesis, JAIST, 2000.
K. Kusakari, M. Nakamura, and Y. Toyama. Argument filtering transformation. In Proc. 1st PPDP, volume 1702 of LNCS, pages 48–62, 1999.
K. Kusakari and Y. Toyama. On proving AC-termination by AC-dependency pairs. Research Report IS-RR-98-0026F, School of Information Science, JAIST, 1998.
D. Lankford. On proving term rewriting systems are noetherian. Report MTP-3, Louisiana Technical University, 1979.
C. Marché and X. Urbain. Termination of associative-commutative rewriting by dependency pairs. In Proc. 9th RTA, volume 1379 of LNCS, pages 241–255, 1998.
T. Nagaya and Y. Toyama. Decidability for left-linear growing term rewriting systems. In Proc. 10th RTA, volume 1631 of LNCS, pages 256–270, 1999.
T. Takai, Y. Kaji, and H. Seki. Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In Proc. 11th RTA, volume 1833 of LNCS, pages 246–260, 2000.
S. Tison. Tree automata and term rewrite systems, July 2000. Invited tutorial at the 11th RTA.
H. Zantema. Termination of term rewriting: Interpretation and type elimination. Journal of Symbolic Computation, 17:23–50, 1994.
H. Zantema. Termination of term rewriting by semantic labelling. Fundamenta Informaticae, 24:89–105, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Middeldorp, A. (2001). Approximating Dependency Graphs Using Tree Automata Techniques. In: Goré, R., Leitsch, A., Nipkow, T. (eds) Automated Reasoning. IJCAR 2001. Lecture Notes in Computer Science, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45744-5_49
Download citation
DOI: https://doi.org/10.1007/3-540-45744-5_49
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42254-9
Online ISBN: 978-3-540-45744-2
eBook Packages: Springer Book Archive