Abstract
Polynomial interpretations are one of the most popular techniques for automated termination analysis and the search for such interpretations is a main bottleneck in most termination provers. We show that one can obtain speedups in orders of magnitude by encoding this task as a SAT problem and by applying modern SAT solvers.
Supported by the DFG (Deutsche Forschungsgemeinschaft) grant GI 274/5-1 and the FWF (Austrian Science Fund) project P18763.
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References
Annov, E., et al.: A SAT-based implementation for RPO termination. In: Short Papers of LPAR ’06 (2006)
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)
Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-09, RWTH Aachen (2001)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge (1998)
Codish, M., Lagoon, V., Stuckey, P.: Solving partial order constraints for LPO termination. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 4–18. Springer, Heidelberg (2006)
Codish, M., et al.: SAT solving for argument filterings. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 30–44. Springer, Heidelberg (2006)
Contejean, E., et al.: CiME, http://cime.lri.fr
Contejean, E., et al.: Mechanically proving termination using polynomial interpretations. J. Aut. Reason. 34(4), 325–363 (2005)
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)
Empirical evaluation of “SAT solving for termination analysis with polynomial interpretations”, http://aprove.informatik.rwth-aachen.de/eval/SATPOLO
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 DP 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., et al.: 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)
Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic termination proofs in the DP framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)
Giesl, J., et al.: Mechanizing and improv- ing dependency pairs. Journal of Automated Reasoning 37(3), 155–203 (2006)
Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. Information and Computation 199(1-2), 172–199 (2005)
Hirokawa, N., Middeldorp, A.: Tyrolean termination tool: Techniques and features. Information and Computation 205(4), 474–511 (2007)
Hofbauer, D., Waldmann, J.: Termination of string rewriting with matrix interpretations. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 328–342. Springer, Heidelberg (2006)
Hong, H., Jakuš, D.: Testing positiveness of polynomials. JAR 21(1), 23–38 (1998)
Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)
Le Berre, D., et al.: SAT4J satisfiability library for Java, http://www.sat4j.org
Giesl, J., et al.: Automated Termination Analysis for Logic Programs by Term Rewriting. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 177–193. Springer, Heidelberg (2007)
Sheini, H.M., Sakallah, K.A.: Pueblo: A hybrid pseudo-boolean SAT solver. Journal on Satisfiability, Boolean Modeling and Computation 2, 61–96 (2006)
Tseitin, G.: On the complexity of derivation in propositional calculus. In: Studies in Constructive Mathematics and Mathematical Logic, pp. 115–125 (1968)
Zankl, H., Hirokawa, N., Middeldorp, A.: Constraints for argument filterings. In: van Leeuwen, J., et al. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 579–590. Springer, Heidelberg (2007)
Zankl, H., Middeldorp, A.: KBO as a satisfaction problem. In: Proc. WST’06 (2006)
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Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H. (2007). SAT Solving for Termination Analysis with Polynomial Interpretations. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_33
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DOI: https://doi.org/10.1007/978-3-540-72788-0_33
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