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Learning Pomset Automata

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12650)

Abstract

We extend the \(\mathtt {L}^{\!\star }\) algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata.

This work was partially supported by the ERC Starting Grant ProFoundNet (679127) and the EPSRC Standard Grant CLeVer (EP/S028641/1). The authors thank Matteo Sammartino for useful discussions.

References

  1. Aarts, F., Vaandrager, F.W.: Learning I/O automata. In: CONCUR. pp. 71–85 (2010). https://doi.org/10.1007/978-3-642-15375-4_6

  2. Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987). https://doi.org/10.1016/0890-5401(87)90052-6

  3. Barlocco, S., Kupke, C.: Angluin learning via logic. In: LFCS. LNCS, vol. 10703, pp. 72–90. Springer (2018). https://doi.org/10.1007/978-3-319-72056-2_5

  4. Bojanczyk, M.: Recognisable languages over monads. In: DLT. pp. 1–13 (2015). https://doi.org/10.1007/978-3-319-21500-6_1

  5. Chapman, M., Chockler, H., Kesseli, P., Kroening, D., Strichman, O., Tautschnig, M.: Learning the language of error. In: ATVA. pp. 114–130 (2015). https://doi.org/10.1007/978-3-319-24953-7_9

  6. Clark, A.: Distributional learning of some context-free languages with a minimally adequate teacher. In: ICGI. pp. 24–37 (2010). https://doi.org/10.1007/978-3-642-15488-1_4

  7. Drewes, F., Högberg, J.: Learning a regular tree language from a teacher. In: DLT. pp. 279–291 (2003). https://doi.org/10.1007/3-540-45007-6_22

  8. Drewes, F., Högberg, J.: Query learning of regular tree languages: How to avoid dead states. Theory Comput. Syst. 40, 163–185 (2007). https://doi.org/10.1007/s00224-005-1233-3

  9. Ésik, Z., Németh, Z.L.: Higher dimensional automata. J. Autom. Lang. Comb. 9(1), 3–29 (2004). https://doi.org/10.25596/jalc-2004-003

  10. Fahrenberg, U., Johansen, C., Struth, G., Thapa, R.B.: Generating posets beyond \(\sf N\). In: RAMiCS. pp. 82–99 (2020). https://doi.org/10.1007/978-3-030-43520-2_6

  11. Ginsburg, S., Spanier, E.H.: Bounded ALGOL-like languages. Trans. Am. Math. Soc. 113(2), 333–368 (1964). https://doi.org/10.2307/1994067

  12. Gischer, J.L.: The equational theory of pomsets. Theor. Comput. Sci. 61, 199–224 (1988). https://doi.org/10.1016/0304-3975(88)90124-7

  13. Grabowski, J.: On partial languages. Fundam. Inform. 4(2), 427 (1981)

    Google Scholar 

  14. van Heerdt, G.: Efficient Inference of Mealy Machines. Bachelor’s thesis, Radboud University (2014), https://www.cs.ru.nl/bachelors-theses/2014/Gerco_van_Heerdt___4167503___Efficient_Inference_of_Mealy_Machines.pdf

  15. van Heerdt, G., Kappé, T., Rot, J., Silva, A.: Learning pomset automata (2021), to appear on arXiv.

    Google Scholar 

  16. van Heerdt, G., Kupke, C., Rot, J., Silva, A.: Learning weighted automata over principal ideal domains. In: FOSSACS. pp. 602–621 (2020). https://doi.org/10.1007/978-3-030-45231-5_31

  17. Hoare, T., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra. In: Proc. Concurrency Theory (CONCUR). pp. 399–414 (2009). https://doi.org/10.1007/978-3-642-04081-8_27

  18. Howar, F., Steffen, B.: Active automata learning in practice - an annotated bibliography of the years 2011 to 2016. In: Machine Learning for Dynamic Software Analysis. pp. 123–148 (2018). https://doi.org/10.1007/978-3-319-96562-8_5

  19. Isberner, M., Howar, F., Steffen, B.: The TTT algorithm: A redundancy-free approach to active automata learning. In: RV. LNCS, vol. 8734, pp. 307–322. Springer (2014). https://doi.org/10.1007/978-3-319-11164-3_26

  20. Isberner, M., Howar, F., Steffen, B.: The open-source learnlib - A framework for active automata learning. In: CAV. pp. 487–495 (2015). https://doi.org/10.1007/978-3-319-21690-4_32

  21. Kappé, T., Brunet, P., Luttik, B., Silva, A., Zanasi, F.: Brzozowski goes concurrent - A Kleene theorem for pomset languages. In: CONCUR. pp. 25:1–25:16 (2017). https://doi.org/10.4230/LIPIcs.CONCUR.2017.25

  22. Kappé, T., Brunet, P., Luttik, B., Silva, A., Zanasi, F.: Equivalence checking for weak bi-Kleene algebra (2018), https://arxiv.org/abs/1807.02102, under submission

  23. Kappé, T., Brunet, P., Luttik, B., Silva, A., Zanasi, F.: On series-parallel pomset languages: Rationality, context-freeness and automata. J. Log. Algebr. Meth. Program. 103, 130–153 (2019). https://doi.org/10.1016/j.jlamp.2018.12.001

  24. Kappé, T., Brunet, P., Silva, A., Zanasi, F.: Concurrent Kleene algebra: Free model and completeness. In: ESOP. pp. 856–882 (2018). https://doi.org/10.1007/978-3-319-89884-1_30

  25. Kearns, M.J., Vazirani, U.V.: An Introduction to Computational Learning Theory. MIT press (1994)

    Google Scholar 

  26. Laurence, M.R., Struth, G.: Completeness theorems for bi-Kleene algebras and series-parallel rational pomset languages. In: Proc. Relational and Algebraic Methods in Computer Science (RAMiCS). pp. 65–82 (2014). https://doi.org/10.1007/978-3-319-06251-8_5

  27. Lodaya, K., Weil, P.: A Kleene iteration for parallelism. In: FSTTCS. pp. 355–366 (1998). https://doi.org/10.1007/978-3-540-49382-2_33

  28. Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theoretical Computer Science 237(1), 347–380 (2000). https://doi.org/10.1016/S0304-3975(00)00031-1

  29. Maler, O., Pnueli, A.: On the learnability of infinitary regular sets. Inf. Comput. 118, 316–326 (1995). https://doi.org/10.1006/inco.1995.1070

  30. Parikh, R.: On context-free languages. J. ACM 13(4), 570–581 (1966). https://doi.org/10.1145/321356.321364

  31. Sakakibara, Y.: Learning context-free grammars from structural data in polynomial time. Theor. Comput. Sci. 76(2-3), 223–242 (1990). https://doi.org/10.1016/0304-3975(90)90017-C

  32. Urbat, H., Adámek, J., Chen, L., Milius, S.: Eilenberg theorems for free. In: MFCS. pp. 43:1–43:15 (2017). https://doi.org/10.4230/LIPIcs.MFCS.2017.43

  33. Urbat, H., Schröder, L.: Automata learning: An algebraic approach. In: LICS. pp. 900–914 (2020). https://doi.org/10.1145/3373718.3394775

  34. Vaandrager, F.W.: Model learning. Commun. ACM 60(2), 86–95 (2017). https://doi.org/10.1145/2967606

  35. Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM J. Comput. 11(2), 298–313 (1982). https://doi.org/10.1137/0211023

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van Heerdt, G., Kappé, T., Rot, J., Silva, A. (2021). Learning Pomset Automata. In: Kiefer, S., Tasson, C. (eds) Foundations of Software Science and Computation Structures. FOSSACS 2021. Lecture Notes in Computer Science(), vol 12650. Springer, Cham. https://doi.org/10.1007/978-3-030-71995-1_26

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  • DOI: https://doi.org/10.1007/978-3-030-71995-1_26

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