Abstract
We propose a query learning algorithm for constructing a minimal DSFA M that separates given two regular languages \(L_+\) and \(L_-\), i.e., \(L_+ \subseteq \mathcal {L}(M)\) and \(L_- \cap \mathcal {L}(M) = \emptyset \). Our algorithm extends the algorithm for learning separating DFAs by Chen et al. (TACAS 2009) embedding the algorithm for learning DSFAs by Argyros and D’Antoni (CAV 2018). Since the problem of finding a minimal separating automaton is NP-hard, we also propose two heuristic methods to learn a separating DSFA which is not necessarily minimal. One runs faster and the other outputs smaller separating DSFAs. So, one of those can be chosen depending on the application requirement.
D. Hendrian—He is currently working in Tokyo Medical and Dental University.
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Notes
- 1.
Argyros and D’Antoni’s theorem claims a less tight bound \(\mathcal {O}(|Q|^2 |\varDelta | \mathcal {M}^\varLambda (k) + |Q|^2 \log m |\varDelta | \mathcal {E}^\varLambda (k))\) but they proved the bound presented here.
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References
Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)
Argyros, G., D’Antoni, L.: The learnability of symbolic automata. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 427–445. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_23
Argyros, G., Stais, I., Kiayias, A., Keromytis, A.D.: Back in black: towards formal, black box analysis of sanitizers and filters. In: IEEE Symposium on Security and Privacy, pp. 91–109 (2016)
Chen, Y.-F., Farzan, A., Clarke, E.M., Tsay, Y.-K., Wang, B.-Y.: Learning minimal separating DFA’s for compositional verification. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 31–45. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00768-2_3
Drews, S., D’Antoni, L.: Learning symbolic automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 173–189. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_10
Gold, E.M.: Complexity of automaton identification from given data. Inf. Control 37(3), 302–320 (1978)
de la Higuera, C.: Grammatical Inference: Learning Automata and Grammars. Cambridge University Press, Cambridge (2010)
Isberner, M.: Foundations of active automata learning: an algorithmic perspective. Ph.D. thesis, Technical University of Dortmund (2015)
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
Leucker, M., Neider, D.: Learning minimal deterministic automata from inexperienced teachers. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012. LNCS, vol. 7609, pp. 524–538. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34026-0_39
Maler, O., Mens, I.-E.: A generic algorithm for learning symbolic automata from membership queries. In: Aceto, L., Bacci, G., Bacci, G., Ingólfsdóttir, A., Legay, A., Mardare, R. (eds.) Models, Algorithms, Logics and Tools. LNCS, vol. 10460, pp. 146–169. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63121-9_8
Moeller, M., Wiener, T., Solko-Breslin, A., Koch, C., Foster, N., Silva, A.: Automata learning with an incomplete teacher (artifact). Dagstuhl Artifacts Ser. 9(2), 21:1–21:3 (2023)
Moon, J., Moser, L.: On cliques in graphs. Israel J. Math. 3, 23–28 (1965)
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
Paull, M.C., Unger, S.H.: Minimizing the number of states in incompletely specified sequential switching functions. IRE Trans. Electron. Comput. EC–8(3), 356–367 (1959)
Acknowledgment
The authors are grateful to the anonymous reviewers for their helpful comments. This work is supported in part by JSPS KAKENHI Grant Numbers JP18K11150 (RY), JP20H05703 (RY), and JP21K11745 (AS).
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Kawasaki, Y., Hendrian, D., Yoshinaka, R., Shinohara, A. (2024). Query Learning of Minimal Deterministic Symbolic Finite Automata Separating Regular Languages. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_24
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