Abstract
To check a system, some verification techniques consider a set of terms \(I\) that represents the initial configurations of the system, and a rewrite system \(R\) that represents the system behavior. To check that no undesirable configuration is reached, they compute an over-approximation of the set of descendants (successors) issued from \(I\) by \(R\), expressed by a tree language. Their success highly depends on the quality of the approximation. Some techniques have been presented using regular tree languages, and more recently using non-regular languages to get better approximations: using context-free tree languages [16] on the one hand, using synchronized tree languages [2] on the other hand. In this paper, we merge these two approaches to get even better approximations: we compute an over-approximation of the descendants, using synchronized-context-free tree languages expressed by logic programs. We give several examples for which our procedure computes the descendants in an exact way, whereas the former techniques compute a strict over-approximation.
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References
Boichut, Y., Boyer, B., Genet, T., Legay, A.: Equational Abstraction Refinement for Certified Tree Regular Model Checking. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 299–315. Springer, Heidelberg (2012)
Boichut, Y., Chabin, J., Réty, P.: Over-approximating descendants by synchronized tree languages. RTA. LIPIcs 21, 128–142 (2013)
Boichut, Y., Chabin, J., Réty, P.: Towards more precise rewriting approximations (full version). Tech. Rep. RR-2014-02, LIFO, Université d’Orléans (2014)
Boichut, Y., Courbis, R., Héam, P.-C., Kouchnarenko, O.: Finer Is Better: Abstraction Refinement for Rewriting Approximations. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 48–62. Springer, Heidelberg (2008)
Boichut, Y., Héam, P.C.: A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations. IPL 108(1), 1–2 (2008)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract Regular (Tree) Model Checking. STTT 14(2), 167–191 (2012)
Comon, H., Dauchet, M., Gilleron, R., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (TATA)
Durand, I., Sylvestre, M.: Left-linear bounded trss are inverse recognizability preserving. RTA. LIPIcs 10, 361–376 (2011)
Engelfriet, J., Heyker, L.: Context-free Hypergraph Grammars have the same Term-generating Power as Attribute Grammars. Acta Informatica 29 (1992)
Engelfriet, J., Vereijken, J.: Context-free Grammars and Concatenation of Graphs. Acta Informatica 34, 773–803 (1997)
Engelfriet, J., Schmidt, E.M.: IO and OI (I). Journal of Computer and System Sciences 15(3), 328–353 (1977)
Engelfriet, J., Schmidt, E.M.: IO and OI (II). Journal of Computer and System Sciences 16(1), 67–99 (1978)
Genet, T.: Decidable Approximations of Sets of Descendants and Sets of Normal Forms. In: Nipkow, T. (ed.) RTA 1998. LNCS, vol. 1379, pp. 151–165. Springer, Heidelberg (1998)
Genet, T., Klay, F.: Rewriting for cryptographic protocol verification. In: McAllester, D. (ed.) Automated Deduction - CADE-17. LNCS, vol. 1831, pp. 271–290. Springer, Heidelberg (2000)
Gouranton, V., Réty, P., Seidl, H.: Synchronized Tree Languages Revisited and New Applications. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 214–229. Springer, Heidelberg (2001)
Kochems, J., Ong, C.H.L.: Improved Functional Flow and Reachability Analyses Using Indexed Linear Tree Grammars. RTA. LIPIcs 10, 187–202 (2011)
Limet, S., Salzer, G.: Proving Properties of Term Rewrite Systems via Logic Programs. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 170–184. Springer, Heidelberg (2004)
Limet, S., Salzer, G.: Tree Tuple Languages from the Logic Programming Point of View. Journal of Automated Reasoning 37(4), 323–349 (2006)
Raoult, J.: Rational Tree Relations. Bulletin of the Belgian Mathematical Society Simon Stevin 4, 149–176 (1997)
Réty, P.: Langages synchronisés d’arbres et applications. Habilitation Thesis (in French). LIFO, Université d’Orléans. Tech. rep., June 2001
Réty, P., Chabin, J., Chen, J.: R-Unification thanks to Synchronized-Contextfree Tree Languages. In: UNIF (2005)
Réty, P., Chabin, J., Chen, J.: Synchronized ContextFree Tree-tuple Languages. Tech. Rep. RR-2006-13 (LIFO, 2006)
Rounds, W.C.: Context-free grammars on trees. In: Fischer, P.C., Ginsburg, S., Harrison, M.A. (eds.) STOC. ACM (1969)
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Boichut, Y., Chabin, J., Réty, P. (2015). Towards More Precise Rewriting Approximations. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_51
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DOI: https://doi.org/10.1007/978-3-319-15579-1_51
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