Abstract
We explore an approach to model learning that is based on using satisfiability modulo theories (SMT) solvers. To that end, we explain how DFAs, Mealy machines and register automata, and observations of their behavior can be encoded as logic formulas. An SMT solver is then tasked with finding an assignment for such a formula, from which we can extract an automaton of minimal size. We provide an implementation of this approach which we use to conduct experiments on a series of benchmarks. These experiments address both the scalability of the approach and its performance relative to existing active learning tools.
This work is supported by the Netherlands Organization for Scientific Research (NWO) projects 628.001.009 on Learning Extended State Machine for Malware Analysis (LEMMA), and 612.001.216 on Active Learning of Security Protocols (ALSeP). This paper greatly extends earlier work [24].
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References
Aarts, F., et al.: Generating models of infinite-state communication protocols using regular inference with abstraction. FMSD 46(1), 1–41 (2015)
Aarts, F., Fiterau-Brostean, P., Kuppens, H., Vaandrager, F.: Learning register automata with fresh value generation. In: Leucker, M., Rueda, C., Valencia, F.D. (eds.) ICTAC 2015. LNCS, vol. 9399, pp. 165–183. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25150-9_11. http://www.sws.cs.ru.nl/publications/papers/fvaan/TomteFresh/
Aarts, F., de Ruiter, J., Poll, E.: Formal models of bank cards for free. In: ICST Workshops, pp. 461–468. IEEE (2013)
Aarts, F., Schmaltz, J., Vaandrager, F.: Inference and abstraction of the biometric passport. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6415, pp. 673–686. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16558-0_54
Angluin, D.: Learning regular sets from queries and counterexamples. I&C 75(2), 87–106 (1987)
Angluin, D.: Negative results for equivalence queries. Mach. Learn. 5, 121–150 (1990)
Bruynooghe, M., et al.: Predicate logic as a modeling language: modeling and solving some machine learning and data mining problems with IDP3. TPLP 15(6), 783–817 (2015)
Cassel, S., Howar, F., Jonsson, B., Steffen, B.: Active learning for extended finite state machines. FAOC 28(2), 233–263 (2016)
De Moura, L., Bjørner, N.: Satisfiability modulo theories: introduction and applications. CACM 54(9), 69–77 (2011)
Florêncio, C.C., Verwer, S.: Regular inference as vertex coloring. TCS 558, 18–34 (2014)
Gold, E.: Language identification in the limit. I&C 10(5), 447–474 (1967)
Heule, M., Verwer, S.: Software model synthesis using satisfiability solvers. Empir. Softw. Eng. 18(4), 825–856 (2013)
De la Higuera, C.: Grammatical Inference: Learning Automata and Grammars. Cambridge University Press, Cambridge (2010)
Howar, F., Steffen, B., Jonsson, B., Cassel, S.: Inferring canonical register automata. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 251–266. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27940-9_17
Isberner, M., Howar, F., Steffen, B.: The TTT algorithm: a redundancy-free approach to active automata learning. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 307–322. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11164-3_26
Lee, D., Yannakakis, M.: Testing finite-state machines: state identification and verification. IEEE Trans. Comput. 43(3), 306–320 (1994)
Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines—a survey. Proc. IEEE 84(8), 1090–1123 (1996)
Neider, D.: Computing minimal separating DFAs and regular invariants using SAT and SMT solvers. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, pp. 354–369. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33386-6_28
Peled, D., Vardi, M., Yannakakis, M.: Black box checking. In: FORTE, pp. 225–240. Kluwer (1999)
Petrenko, A., Avellaneda, F., Groz, R., Oriat, C.: From passive to active FSM inference via checking sequence construction. In: Yevtushenko, N., Cavalli, A.R., Yenigün, H. (eds.) ICTSS 2017. LNCS, vol. 10533, pp. 126–141. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67549-7_8
Raffelt, H., Steffen, B., Berg, T., Margaria, T.: LearnLib: a framework for extrapolating behavioral models. STTT 11(5), 393–407 (2009)
Schuts, M., Hooman, J., Vaandrager, F.: Refactoring of legacy software using model learning and equivalence checking: an industrial experience report. In: Ábrahám, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 311–325. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-33693-0_20
Smeenk, W., Moerman, J., Vaandrager, F., Jansen, D.N.: Applying automata learning to embedded control software. In: Butler, M., Conchon, S., Zaïdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 67–83. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25423-4_5
Smetsers, R.: Grammatical Inference as a Satisfiability Modulo Theories Problem. arXiv preprint arXiv:1705.10639 (2017)
Vaandrager, F.: Model learning. CACM 60(2), 86–95 (2017)
Walkinshaw, N., Derrick, J., Guo, Q.: Iterative refinement of reverse-engineered models by model-based testing. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 305–320. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05089-3_20
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Smetsers, R., Fiterău-Broştean, P., Vaandrager, F. (2018). Model Learning as a Satisfiability Modulo Theories Problem. In: Klein, S., Martín-Vide, C., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2018. Lecture Notes in Computer Science(), vol 10792. Springer, Cham. https://doi.org/10.1007/978-3-319-77313-1_14
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