Abstract
We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach is competitive with alternative techniques. Our contributions are fourfold: First, we propose a compact translation of DFA identification into SAT. Second, we reduce the SAT search space by adding lower bound information using a fast max-clique approximation algorithm. Third, we include many redundant clauses to provide the SAT solver with some additional knowledge about the problem. Fourth, we show how to use the flexibility of our translation in order to apply it to very hard problems. Experiments on a well-known suite of random DFA identification problems show that SAT solvers can efficiently tackle all instances. Moreover, our algorithm outperforms state-of-the-art techniques on several hard problems.
This is an extended version of: Marijn Heule and Sicco Verwer. Using a Satisfiability Solver to Identify Deterministic Finite State Automata. In BNAIC 2009, pp. 91-98.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
de la Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 1332–1348 (2005)
Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)
Lang, K.J., Pearlmutter, B.A., Price, R.A.: Results of the abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, p. 1. Springer, Heidelberg (1998)
Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Pattern Recognition and Image Analysis. Series in Machine Perception and Artificial Intelligence, vol. 1, pp. 49–61. World Scientific, Singapore (1992)
Oliveira, A.L., Marques-Silva, J.P.: Efficient search techniques for the inference of minimum sized finite state machines. In: SPIRE, pp. 81–89 (1998)
Abela, J., Coste, F., Spina, S.: Mutually compatible and incompatible merges for the search of the smallest consistent DFA. In: Paliouras, G., Sakakibara, Y. (eds.) ICGI 2004. LNCS (LNAI), vol. 3264, pp. 28–39. Springer, Heidelberg (2004)
Lang, K.J.: Faster algorithms for finding minimal consistent DFAs. Technical report, NEC Research Institute (1999)
Bugalho, M., Oliveira, A.L.: Inference of regular languages using state merging algorithms with search. Pattern Recognition 38, 1457–1467 (2005)
Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Marques-Silva, J.P., Glass, T.: Combinational equivalence checking using satisfiability and recursive learning. In: DATE 1999, p. 33. ACM, New York (1999)
Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(2-3), 195–220 (2008)
Coste, F., Nicolas, J.: Regular inference as a graph coloring problem. In: Workshop on Grammatical Inference, Automata Induction, and Language Acquisition, ICML 1997 (1997)
Grinchtein, O., Leucker, M., Piterman, N.: Inferring network invariants automatically. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 483–497. Springer, Heidelberg (2006)
Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Trans. Comput. 21(6), 592–597 (1972)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Sakallah, K.A.: Symmetry and Satisfiability. In: Handbook of Satisfiability, ch. 10, pp. 289–338. IOS Press, Amsterdam (2009)
Kullmann, O.: On a generalization of extended resolution. Discrete Applied Mathematics 96-97(1), 149–176 (1999)
Jarvisalo, M., Biere, A., Heule, M.J.H.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)
Oliveira, A.L., Marques-Silva, J.P.: Efficient search techniques for the inference of minimum size finite automata. In: South American Symposium on String Processing and Information Retrieval, pp. 81–89. IEEE Computer Society Press, Los Alamitos (1998)
Biere, A.: Picosat essentials. Journal on Satisfiability, Boolean Modeling and Computation 4, 75–97 (2008)
Velev, M.N.: Exploiting hierarchy and structure to efficiently solve graph coloring as sat. In: ICCAD 2007: International conference on Computer-aided design, Piscataway, NJ, USA, pp. 135–142. IEEE Press, Los Alamitos (2007)
Schaafsma, B., Heule, M.J.H., van Maaren, H.: Dynamic symmetry breaking by simulating Zykov contraction. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 223–236. Springer, Heidelberg (2009)
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
Heule, M.J.H., Verwer, S. (2010). Exact DFA Identification Using SAT Solvers. In: Sempere, J.M., García, P. (eds) Grammatical Inference: Theoretical Results and Applications. ICGI 2010. Lecture Notes in Computer Science(), vol 6339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15488-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-15488-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15487-4
Online ISBN: 978-3-642-15488-1
eBook Packages: Computer ScienceComputer Science (R0)