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. 2020 Mar 13;12079:325–343. doi: 10.1007/978-3-030-45237-7_20

Polynomial Identification of Inline graphic-Automata

Dana Angluin 10, Dana Fisman 11,✉, Yaara Shoval 11
Editors: Armin Biere8, David Parker9
PMCID: PMC7480709

Abstract

We study identification in the limit using polynomial time and data for models of Inline graphic-automata. On the negative side we show that non-deterministic Inline graphic-automata (of types Büchi, coBüchi, Parity or Muller) can not be polynomially learned in the limit. On the positive side we show that the Inline graphic-language classes Inline graphic, Inline graphic, Inline graphic, and Inline graphic that are defined by deterministic Büchi, coBüchi, parity, and Muller acceptors that are isomorphic to their right-congruence automata (that is, the right congruences of languages in these classes are fully informative) are identifiable in the limit using polynomial time and data. We further show that for these classes a characteristic sample can be constructed in polynomial time.

Keywords: identification in the limit, characteristic sample, Inline graphic-regular

Footnotes

This research was supported by grant 2016239 from the United States – Israel Binational Science Foundation (BSF).

Contributor Information

Armin Biere, Email: biere@jku.at.

David Parker, Email: d.a.parker@cs.bham.ac.uk.

Dana Fisman, Email: dana@cs.bgu.ac.ll.

References

  • 1.Aarts, F., Vaandrager, F.: Learning I/O automata. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010 - Concurrency Theory: 21th International Conference, CONCUR 2010, Paris, France, August 31-September 3, 2010. Proceedings. pp. 71–85. Springer Berlin Heidelberg, Berlin, Heidelberg (2010)
  • 2.Ammons, G., Bodík, R., Larus, J.R.: Mining specifications. In: Conference Record of POPL 2002: The 29th SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Portland, OR, USA, January 16-18, 2002. pp. 4–16 (2002)
  • 3.Angluin, D., Antonopoulos, T., Fisman, D.: Strongly unambiguous Büchi automata are polynomially predictable with membership queries. In: 28th EACSL Annual Conference on Computer Science Logic, CSL 2020, January 13-16, 2020, Barcelona, Spain. pp. 8:1–8:17 (2020)
  • 4.Angluin, D., Fisman, D.: Regular omega-languages with an informative right congruence. In: GandALF. EPTCS, vol. 277, pp. 265–279 (2018)
  • 5.Angluin D. Learning regular sets from queries and counterexamples. Inf. Comput. 1987;75(2):87–106. [Google Scholar]
  • 6.Angluin, D., Boker, U., Fisman, D.: Families of DFAs as acceptors of omega-regular languages. In: 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, August 22-26, 2016 - Kraków, Poland. pp. 11:1–11:14 (2016)
  • 7.Angluin, D., Fisman, D.: Learning regular omega languages. In: Algorithmic Learning Theory - 25th International Conference, ALT 2014, Bled, Slovenia, October 8-10, 2014. Proceedings. pp. 125–139 (2014)
  • 8.Angluin D, Fisman D. Learning regular omega languages. Theor. Comput. Sci. 2016;650:57–72. [Google Scholar]
  • 9.Angluin, D., Fisman, D.: Polynomial time algorithms for inclusion and equivalence of deterministic omega acceptors. In: arXiv:2002.03191v2, cs.FL (2020)
  • 10.Chalupar, G., Peherstorfer, S., Poll, E., de Ruiter, J.: Automated reverse engineering using Lego®. In: 8th USENIX Workshop on Offensive Technologies (WOOT 14). USENIX Association, San Diego, CA (Aug 2014)
  • 11.Chapman, M., Chockler, H., Kesseli, P., Kroening, D., Strichman, O., Tautschnig, M.: Learning the language of error. In: Automated Technology for Verification and Analysis - 13th International Symposium, ATVA 2015, Shanghai, China, October 12-15, 2015, Proceedings. pp. 114–130 (2015)
  • 12.Cho, C.Y., Babic, D., Shin, E.C.R., Song, D.: Inference and analysis of formal models of botnet command and control protocols. In: Proceedings of the 17th ACM Conference on Computer and Communications Security, CCS 2010, Chicago, Illinois, USA, October 4-8, 2010. pp. 426–439 (2010)
  • 13.Cobleigh, J.M., Giannakopoulou, D., Păsăreanu, C.S.: Learning assumptions for compositional verification. In: Proceedings of the 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. pp. 331–346. TACAS ’03, Springer-Verlag, Berlin, Heidelberg (2003)
  • 14.Drews, D., D’Antoni, L.: Learning symbolic automata. In: Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings, Part I. pp. 173–189 (2017)
  • 15.Farzan, A., Chen, Y.F., Clarke, E., Tsay, Y.K., Wang, B.Y.: Extending automated compositional verification to the full class of omega-regular languages. In: TACAS. pp. 2–17 (2008)
  • 16.Gold EM. Complexity of automaton identification from given data. Information and Control. 1978;37(3):302–320. [Google Scholar]
  • 17.Goldman SA, Mathias HD. Teaching a smarter learner. J. Comput. Syst. Sci. 1996;52(2):255–267. [Google Scholar]
  • 18.Habermehl P, Vojnar T. Regular model checking using inference of regular languages. Electr. Notes Theor. Comput. Sci. 2005;138(3):21–36. [Google Scholar]
  • 19.de la Higuera C. Characteristic sets for polynomial grammatical inference. Machine Learning. 1997;27(2):125–138. [Google Scholar]
  • 20.Howar, F., Steffen, B., Jonsson, B., Cassel, S.: Inferring canonical register automata. In: Verification, Model Checking, and Abstract Interpretation - 13th International Conference, VMCAI 2012, Philadelphia, PA, USA, January 22-24, 2012. Proceedings. pp. 251–266 (2012)
  • 21.Kupferman O, Vardi MY, Wolper P. An automata-theoretic approach to branching-time model checking. J. ACM. 2000;47(2):312–360. [Google Scholar]
  • 22.Li, Y., Chen, Y., Zhang, L., Liu, D.: A novel learning algorithm for büchi automata based on family of dfas and classification trees. In: Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings, Part I. pp. 208–226 (2017)
  • 23.Maler O, Pnueli A. On the learnability of infinitary regular sets. Inf. Comput. 1995;118(2):316–326. [Google Scholar]
  • 24.Maler, O., Pnueli, A.: On the learnability of infinitary regular sets. In: Proceedings of the Fourth Annual Workshop on Computational Learning Theory, COLT 1991, Santa Cruz, California, USA, August 5-7, 1991. pp. 128–136 (1991)
  • 25.Manevich, R., Shoham, S.: Inferring program extensions from traces. In: ICGI. Proceedings of Machine Learning Research, vol. 93, pp. 139–154. PMLR (2018)
  • 26.Margaria, T., Niese, O., Raffelt, H., Steffen, B.: Efficient test-based model generation for legacy reactive systems. In: HLDVT. pp. 95–100. IEEE Computer Society (2004)
  • 27.Nam, W., Alur, R.: Learning-based symbolic assume-guarantee reasoning with automatic decomposition. In: ATVA. Lecture Notes in Computer Science, vol. 4218, pp. 170–185. Springer (2006)
  • 28.Peled, D., Vardi, M.Y., Yannakakis, M.: Black box checking. In: FORTE. pp. 225–240 (1999)
  • 29.Schuts, M., Hooman, J., Vaandrager, F.W.: Refactoring of legacy software using model learning and equivalence checking: An industrial experience report. In: Integrated Formal Methods - 12th International Conference, IFM 2016, Reykjavik, Iceland, June 1-5, 2016, Proceedings. pp. 311–325 (2016)
  • 30.Staiger L. Finite-state omega-languages. J. Comput. Syst. Sci. 1983;27(3):434–448. [Google Scholar]
  • 31.Vaandrager F. Model learning. Commun. ACM. 2017;60(2):86–95. [Google Scholar]
  • 32.Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Using language inference to verify omega-regular properties. In: Tools and Algorithms for the Construction and Analysis of Systems, 11th International Conference, TACAS 2005, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2005, Edinburgh, UK, April 4-8, 2005, Proceedings. pp. 45–60 (2005)
  • 33.Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Banff Higher Order Workshop. Lecture Notes in Computer Science, vol. 1043, pp. 238–266. Springer (1995)
  • 34.Wagner, K.W.: A hierarchy of regular sequence sets. In: 4th Symposium on Mathematical Foundations of Computer (MFCS). pp. 445–449 (1975)

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