Learning Deterministic Visibly Pushdown Automata Under Accessible Stack

Authors Jakub Michaliszyn , Jan Otop



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Jakub Michaliszyn
  • University of Wrocław, Poland
Jan Otop
  • University of Wrocław, Poland

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Jakub Michaliszyn and Jan Otop. Learning Deterministic Visibly Pushdown Automata Under Accessible Stack. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 74:1-74:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.74

Abstract

We study the problem of active learning deterministic visibly pushdown automata. We show that in the classical L^*-setting, efficient active learning algorithms are not possible. To overcome this difficulty, we propose the accessible stack setting, where the algorithm has the read and write access to the stack. In this setting, we show that active learning can be done in polynomial time in the size of the target automaton and the counterexamples provided by the teacher. As counterexamples of exponential size are inevitable, we consider an algorithm working with words in a compressed representation via (visibly) Straight-Line Programs. Employing compression allows us to obtain an algorithm where the teacher and the learner work in time polynomial in the size of the target automaton alone.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • visibly pushdown automata
  • automata inference
  • minimization

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References

  1. Rajeev Alur, Ahmed Bouajjani, and Javier Esparza. Model checking procedural programs. In Handbook of Model Checking, pages 541-572. Springer, 2018. Google Scholar
  2. Rajeev Alur, Kousha Etessami, and Parthasarathy Madhusudan. A temporal logic of nested calls and returns. In TACAS, pages 467-481. Springer, 2004. Google Scholar
  3. Rajeev Alur, Viraj Kumar, Parthasarathy Madhusudan, and Mahesh Viswanathan. Congruences for visibly pushdown languages. In ICALP 2005, pages 1102-1114. Springer, 2005. Google Scholar
  4. Rajeev Alur and P. Madhusudan. Adding nesting structure to words. J. ACM, 56(3):16:1-16:43, 2009. URL: https://doi.org/10.1145/1516512.1516518.
  5. Dana Angluin. Learning k-bounded context-free grammars. Research report. Yale University. Dept. of Computer Science, 557, 1987. Google Scholar
  6. Dana Angluin. Learning regular sets from queries and counterexamples. Information and computation, 75(2):87-106, 1987. Google Scholar
  7. Dana Angluin and Michael Kharitonov. When won't membership queries help? J. Comput. Syst. Sci., 50(2):336-355, 1995. Google Scholar
  8. Borja Balle and Mehryar Mohri. Learning weighted automata. In CAI 2015, pages 1-21, 2015. Google Scholar
  9. Borja Balle and Mehryar Mohri. On the Rademacher complexity of weighted automata. In ALT 2015, pages 179-193, 2015. Google Scholar
  10. Borja Balle and Mehryar Mohri. Generalization bounds for learning weighted automata. Theor. Comput. Sci., 716:89-106, 2018. Google Scholar
  11. Borja Balle, Prakash Panangaden, and Doina Precup. A canonical form for weighted automata and applications to approximate minimization. In LICS 2015, pages 701-712, 2015. Google Scholar
  12. Benoît Barbot, Benedikt Bollig, Alain Finkel, Serge Haddad, Igor Khmelnitsky, Martin Leucker, Daniel Neider, Rajarshi Roy, and Lina Ye. Extracting context-free grammars from recurrent neural networks using tree-automata learning and a* search. In Jane Chandlee, Rémi Eyraud, Jeff Heinz, Adam Jardine, and Menno Zaanen, editors, Proceedings of the 15th International Conference on Grammatical Inference, 23-27 August 2021, Virtual Event, volume 153 of Proceedings of Machine Learning Research, pages 113-129. PMLR, 2021. URL: https://proceedings.mlr.press/v153/barbot21a.html.
  13. Jean Berstel and Luc Boasson. Towards an algebraic theory of context-free languages. Fundamenta Informaticae, 25(3, 4):217-239, 1996. Google Scholar
  14. Armin Biere, Alessandro Cimatti, Edmund M. Clarke, Ofer Strichman, and Yunshan Zhu. Bounded model checking. Adv. Comput., 58:117-148, 2003. URL: https://doi.org/10.1016/S0065-2458(03)58003-2.
  15. Laura Bozzelli, Aniello Murano, and Adriano Peron. Context-free timed formalisms: Robust automata and linear temporal logics. Information and Computation, page 104673, 2020. Google Scholar
  16. Swarat Chaudhuri and Rajeev Alur. Instrumenting c programs with nested word monitors. In International SPIN Workshop on Model Checking of Software, pages 279-283. Springer, 2007. Google Scholar
  17. Patrick Chervet and Igor Walukiewicz. Minimizing variants of visibly pushdown automata. In MFCS 2007, volume 4708 of Lecture Notes in Computer Science, pages 135-146. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74456-6_14.
  18. Hana Chockler, Pascal Kesseli, Daniel Kroening, and Ofer Strichman. Learning the language of software errors. J. Artif. Intell. Res., 67:881-903, 2020. URL: https://doi.org/10.1613/jair.1.11798.
  19. Colin de la Higuera. Grammatical Inference: Learning Automata and Grammars. Cambridge University Press, New York, NY, USA, 2010. Google Scholar
  20. Olivier Gauwin, Anca Muscholl, and Michael Raskin. Minimization of visibly pushdown automata is np-complete. Log. Methods Comput. Sci., 16(1), 2020. Google Scholar
  21. Dimitra Giannakopoulou, Kedar S. Namjoshi, and Corina S. Pasareanu. Compositional reasoning. In Handbook of Model Checking, pages 345-383. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-10575-8_12.
  22. David Hopkins, Andrzej S Murawski, and C-H Luke Ong. A fragment of ML decidable by visibly pushdown automata. In ICALP, pages 149-161. Springer, 2011. Google Scholar
  23. Malte Isberner. Foundations of Active Automata Learning: An Algorithmic Perspective. PhD thesis, Technischen Universität Dortmund, 2015. URL: https://eldorado.tu-dortmund.de/bitstream/2003/34282/1/Dissertation.pdf.
  24. Petr Jancar. Equivalence of pushdown automata via first-order grammars. J. Comput. Syst. Sci., 115:86-112, 2021. URL: https://doi.org/10.1016/j.jcss.2020.07.004.
  25. Kareem Khazem and Michael Tautschnig. CBMC path: A symbolic execution retrofit of the C bounded model checker. In TACAS, volume 11429 of LNCS, pages 199-203, 2019. URL: https://doi.org/10.1007/978-3-030-17502-3_13.
  26. Bruce Knobe and Kathleen Knobe. A method for inferring context-free grammars. Information and Control, 31(2):129-146, 1976. Google Scholar
  27. Viraj Kumar, P. Madhusudan, and Mahesh Viswanathan. Minimization, learning, and conformance testing of boolean programs. In CONCUR 2006, pages 203-217. Springer Berlin Heidelberg, 2006. Google Scholar
  28. Christof Löding, Parthasarathy Madhusudan, and Olivier Serre. Visibly pushdown games. In FSTTCS, pages 408-420. Springer, 2004. Google Scholar
  29. Markus Lohrey. Leaf languages and string compression. Inf. Comput., 209(6):951-965, 2011. URL: https://doi.org/10.1016/j.ic.2011.01.009.
  30. Markus Lohrey. Algorithmics on SLP-compressed strings: A survey. Groups-Complexity-Cryptology, 4(2):241-299, 2012. Google Scholar
  31. Wim Martens, Frank Neven, Thomas Schwentick, and Geert Jan Bex. Expressiveness and complexity of XML schema. ACM Transactions on Database Systems (TODS), 31(3):770-813, 2006. Google Scholar
  32. Ines Marusic and James Worrell. Complexity of equivalence and learning for multiplicity tree automata. Journal of Machine Learning Research, 16:2465-2500, 2015. Google Scholar
  33. Kurt Mehlhorn. Pebbling mountain ranges and its application of DCFL-recognition. In ICALP 1980, volume 85 of LNCS, pages 422-435. Springer, 1980. URL: https://doi.org/10.1007/3-540-10003-2_89.
  34. Jakub Michaliszyn and Jan Otop. Approximate learning of limit-average automata. In CONCUR 2019, pages 17:1-17:16, 2019. URL: https://doi.org/10.4230/LIPIcs.CONCUR.2019.17.
  35. Jakub Michaliszyn and Jan Otop. Learning deterministic automata on infinite words. In ECAI 2020 - 24th European Conference on Artificial Intelligence, volume 325, pages 2370-2377. IOS Press, 2020. URL: https://doi.org/10.3233/FAIA200367.
  36. Jakub Michaliszyn and Jan Otop. Non-deterministic weighted automata evaluated over Markov chains. J. Comput. Syst. Sci., 108:118-136, 2020. Google Scholar
  37. Marvin C Paull and Stephen H Unger. Structural equivalence of context-free grammars. J. Comput. Syst. Sci., 2(4):427-463, 1968. Google Scholar
  38. Doron Peled. Partial-order reduction. In Handbook of Model Checking, pages 173-190. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-10575-8_6.
  39. Daniel J. Rosenkrantz and Harry B. Hunt III. The complexity of structural containment and equivalence. In Jeffrey D. Ullman, editor, Theoretical Studies in Computer Science, to Seymour Ginsburg on the occasion of his 2^6. birthday, pages 101-132. Academic Press, 1992. URL: https://doi.org/10.1016/b978-0-12-708240-0.50009-5.
  40. Yasubumi Sakakibara. Efficient learning of context-free grammars from positive structural examples. Information and Computation, 97(1):23-60, 1992. Google Scholar
  41. Géraud Sénizergues. The equivalence problem for deterministic pushdown automata is decidable. In ICALP 1997, pages 671-681, 1997. URL: https://doi.org/10.1007/3-540-63165-8_221.
  42. Luzi Sennhauser and Robert C. Berwick. Evaluating the ability of LSTMs to learn context-free grammars. In Proceedings of the Workshop: Analyzing and Interpreting Neural Networks for NLP, BlackboxNLP@EMNLP 2018, pages 115-124, 2018. URL: https://doi.org/10.18653/v1/w18-5414.
  43. Ehud Y Shapiro. Algorithmic program diagnosis. In POPL, pages 299-308, 1982. Google Scholar
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