Abstract
This paper combines predictive labeling with dependency pairs and reports on its implementation. Our starting point is the method of proving termination of rewrite systems using semantic labeling with infinite models in combination with lexicographic path orders. We replace semantic labeling with predictive labeling to weaken the quasi-model constraints and we combine it with dependency pairs (usable rules and argument filtering) to increase the power of the method. Encoding the resulting search problem as a propositional satisfiability problem and calling a state-of-the-art SAT solver yields a powerful technique for proving termination automatically.
This is a preview of subscription content, log in via an institution to check access.
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
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. TCS 236, 133–178 (2000)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Codish, M., Schneider-Kamp, P., Lagoon, V., Thiemann, R., Giesl, J.: SAT solving for argument filterings. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 30–44. Springer, Heidelberg (2006)
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 574–588. Springer, Heidelberg (2006)
Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)
Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. JAR 37(3), 155–203 (2006)
Gramlich, B.: Generalized sufficient conditions for modular termination of rewriting. AAECC 5, 131–158 (1994)
Hardin, T., Laville, A.: Proof of termination of the rewriting system SUBST on CCL. TCS 46(2-3), 305–312 (1986)
Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. Information and Computation 199(1,2), 172–199 (2005)
Hirokawa, N., Middeldorp, A.: Predictive labeling. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 313–327. Springer, Heidelberg (2006)
Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. Information and Computation 205(4), 474–511 (2007)
Koprowski, A.: TPA: Termination proved automatically. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 257–266. Springer, Heidelberg (2006)
Koprowski, A., Zantema, H.: Automation of recursive path ordering for infinite labelled rewrite systems. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 332–346. Springer, Heidelberg (2006)
Lankford, D.: On proving term rewrite systems are noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)
Ohlebusch, E.: On the modularity of termination of term rewriting systems. TCS 136(2), 333–360 (1994)
Thiemann, R., Giesl, J.: The size-change principle and dependency pairs for termination of term rewriting. AAECC 16(4), 229–270 (2005)
Urbain, X.: Modular & incremental automated termination proofs. JAR 32, 315–355 (2004)
Zankl, H., Hirokawa, N., Middeldorp, A.: Constraints for argument filterings. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 579–590. Springer, Heidelberg (2007)
Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae 24, 89–105 (1995)
Termination problem data base, version 3.2 (2006), http://www.lri.fr/~marche/tpdb
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koprowski, A., Middeldorp, A. (2007). Predictive Labeling with Dependency Pairs Using SAT. In: Pfenning, F. (eds) Automated Deduction – CADE-21. CADE 2007. Lecture Notes in Computer Science(), vol 4603. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73595-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-73595-3_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73594-6
Online ISBN: 978-3-540-73595-3
eBook Packages: Computer ScienceComputer Science (R0)