Abstract
The polynomial path order ( POP* for short) is a termination method that induces polynomial bounds on the innermost runtime complexity of term rewrite systems (TRSs for short). Semantic labeling is a transformation technique used for proving termination.
In this paper, we propose an efficient implementation of POP* together with finite semantic labeling. This automation works by a reduction to the problem of boolean satisfiability. We have implemented the technique and experimental results confirm the feasibility of our approach. By semantic labeling the analytical power of POP* is significantly increased.
This research is supported by FWF (Austrian Science Fund) projects P20133.
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
Anderson, H., Khoo, S., Andrei, S., Luca, B.: Calculating polynomial runtime properties. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 230–246. Springer, Heidelberg (2005)
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. TCS 236(1-2), 133–178 (2000)
Avanzini, M., Hirokawa, N., Middeldorp, A., Moser, G.: Proving termination of scheme programs by rewriting, http://cl-informatik.uibk.ac.at/~zini/publications/SchemeTR07.pdf
Avanzini, M., Moser, G.: Complexity analysis by rewriting. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 130–146. Springer, Heidelberg (2008)
Avanzini, M., Moser, G.: Dependency pairs and polynomial path orders. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 48–62. Springer, Heidelberg (2009)
Avanzini, M., Moser, G.: Polynomial path orders and the rules of predicative recursion with parameter substitution. In: Proc. 10th WST (2009)
Avanzini, M., Moser, G.: Complexity analysis by graph rewriting. In: Proc. 11th FLOPS. LNCS. Springer, Heidelberg (to appear, 2010)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Bellantoni, S., Cook, S.A.: A new recursion-theoretic characterization of the polytime functions. CC 2, 97–110 (1992)
Bonfante, G., Marion, J., Péchoux, R.: Quasi-interpretation synthesis by decomposition. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 410–424. Springer, Heidelberg (2007)
Dershowitz, N.: Orderings for term-rewriting systems. In: 20th Annual Symposium on Foundations of Computer Science, pp. 123–131. IEEE, Los Alamitos (1979)
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)
Giesl, J., Swiderski, S., Schneider-Kamp, P., Thiemann, R.: Automated termination analysis for Haskell: From term rewriting to programming languages. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 297–312. Springer, Heidelberg (2006)
Hirokawa, N., Moser, G.: Automated complexity analysis based on the dependency pair method. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 364–380. Springer, Heidelberg (2008)
Hofbauer, D.: Termination proofs by multiset path orderings imply primitive recursive derivation lengths. TCS 105(1), 129–140 (1992)
Koprowski, A.: Tpa: Termination proved automatically. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 297–312. Springer, Heidelberg (2006)
Koprowski, A., Middeldorp, A.: Predictive labeling with dependency pairs using SAT. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 410–425. Springer, Heidelberg (2007)
Kusakari, K., Nakamura, M., Toyama, Y.: Argument filtering transformation. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 47–61. Springer, Heidelberg (1999)
Lescanne, P.: Termination of rewrite systems by elementary interpretations. Formal Aspects of Computing 7(1), 77–90 (1995)
Moser, G., Schnabl, A.: Proving quadratic derivational complexities using context dependent interpretations. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 276–290. Springer, Heidelberg (2008)
Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. J. Symb. Comput. 2(3), 293–304 (1986)
Rosendahl, M.: Automatic complexity analysis. In: Proc. 4th FPCA, pp. 144–156 (1989)
Schneider-Kamp, P., Thiemann, R., Annov, E., Codish, M., Giesl, J.: Proving termination using recursive path orders and SAT solving. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 267–282. Springer, Heidelberg (2007)
TeReSe: Term Rewriting Systems. CTTCS, vol. 55. Cambridge University Press, Cambridge (2003)
Tseitin, G.: On the complexity of derivation in propositional calculus. SCML, Part 2, 115–125 (1968)
Zantema, H.: Termination of term rewriting by semantic labelling. FI 24(1/2), 89–105 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Avanzini, M. (2010). POP* and Semantic Labeling Using SAT. In: Icard, T., Muskens, R. (eds) Interfaces: Explorations in Logic, Language and Computation. ESSLLI ESSLLI 2008 2009. Lecture Notes in Computer Science(), vol 6211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14729-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-14729-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14728-9
Online ISBN: 978-3-642-14729-6
eBook Packages: Computer ScienceComputer Science (R0)