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Parameterized Synthesis with Safety Properties

  • Oliver MarkgrafEmail author
  • Chih-Duo Hong
  • Anthony W. Lin
  • Muhammad Najib
  • Daniel Neider
Conference paper
  • 104 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12470)

Abstract

Parameterized synthesis offers a solution to the problem of constructing correct and verified controllers for parameterized systems. Such systems occur naturally in practice (e.g., in the form of distributed protocols where the amount of processes is often unknown at design time and the protocol must work regardless of the number of processes). In this paper, we present a novel learning-based approach to the synthesis of reactive controllers for parameterized systems from safety specifications. We use the framework of regular model checking to model the synthesis problem as an infinite-duration two-player game and show how one can utilize Angluin’s well-known L\(^{*}\) algorithm to learn correct-by-design controllers. This approach results in a synthesis procedure that is conceptually simpler than existing synthesis methods with a completeness guarantee, whenever a winning strategy can be expressed by a regular set. We have implemented our algorithm in a tool called L\(^{*}\)-PSynth and have demonstrated its performance on a range of benchmarks, including robotic motion planning and distributed protocols. Despite the simplicity of L\(^{*}\)-PSynth  it competes well against (and in many cases even outperforms) the state-of-the-art tools for synthesizing parameterized systems.

Keywords

Parameterized systems Reactive synthesis Machine learning Angluin’s algorithm Regular model checking 

Notes

Acknowledgement

This work was partially funded by the ERC Starting Grant AV-SMP (grant agreement no. 759969) and MPI-Fellowship as well as the DFG grant no. 434592664.

References

  1. 1.
    Griesmayer, A., Staber, S., Bloem, R.: Automated fault localization for C programs. Electron. Notes Theoret. Comput. Sci. 174(4), 95–111 (2007) CrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Jonsson, B., Mahata, P., d’Orso, J.: Regular tree model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 555–568. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45657-0_47CrossRefGoogle Scholar
  3. 3.
    Abdulla, P.A.: Regular model checking. STTT 14(2), 109–118 (2012).  https://doi.org/10.1007/s10009-011-0216-8CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Haziza, F., Holík, L.: Parameterized verification through view abstraction. STTT 18(5), 495–516 (2016).  https://doi.org/10.1007/s10009-015-0406-xCrossRefzbMATHGoogle Scholar
  5. 5.
    Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87–106 (1987)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Angluin, D., Fisman, D.: Learning regular omega languages. Theor. Comput. Sci. 650, 57–72 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Apt, K.R., Kozen, D.: Limits for automatic verification of finite-state concurrent systems. Inf. Process. Lett. 22(6), 307–309 (1986)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Beyene, T.A., Chaudhuri, S., Popeea, C., Rybalchenko, A.: A constraint-based approach to solving games on infinite graphs. In: Jagannathan, S., Sewell, P. (eds.) The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2014, San Diego, CA, USA, 20–21 January 2014 (2014)Google Scholar
  9. 9.
    Bloem, R., et al.: Decidability of Parameterized Verification. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, San Rafael (2015)CrossRefGoogle Scholar
  10. 10.
    Bollig, B., Habermehl, P., Kern, C., Leucker, M.: Angluin-style learning of NFA. In: IJCAI, pp. 1004–1009Google Scholar
  11. 11.
    Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract regular (tree) model checking. STTT 14(2), 167–191 (2012).  https://doi.org/10.1007/s10009-011-0205-yCrossRefzbMATHGoogle Scholar
  12. 12.
    Bouton, C.L.: Nim, a game with a complete mathematical theory. Ann. Math. 3(1/4), 35–39 (1901). http://www.jstor.org/stable/1967631
  13. 13.
    Camacho, A., Muise, C.J., Baier, J.A., McIlraith, S.A.: LTL realizability via safety and reachability games. In: Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, Stockholm, Sweden, 13–19 July 2018, pp. 4683–4691 (2018)Google Scholar
  14. 14.
    Chatain, T., David, A., Larsen, K.G.: Playing games with timed games. In: 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2009, Zaragoza, Spain, 16–18 September 2009, pp. 238–243 (2009)Google Scholar
  15. 15.
    Chen, Y.-F., Clarke, E.M., Farzan, A., Tsai, M.-H., Tsay, Y.-K., Wang, B.-Y.: Automated assume-guarantee reasoning through implicit learning. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 511–526. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14295-6_44CrossRefGoogle Scholar
  16. 16.
    Chen, Y., Hong, C., Lin, A.W., Rümmer, P.: Learning to prove safety over parameterised concurrent systems. In: Formal Methods in Computer Aided Design, FMCAD 2017, Vienna, Austria, 2–6 October 2017, pp. 76–83 (2017)Google Scholar
  17. 17.
    Doyen, L.: Games and automata: from boolean to quantitative verification. habilitation, ENS de Cachan, LSV (2011)Google Scholar
  18. 18.
    Ehlers, R., Seshia, S.A., Kress-Gazit, H.: Synthesis with identifiers. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 415–433. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54013-4_23CrossRefGoogle Scholar
  19. 19.
    Fang, Y., Piterman, N., Pnueli, A., Zuck, L.: Liveness with incomprehensible ranking. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 482–496. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24730-2_36CrossRefGoogle Scholar
  20. 20.
    Fang, Y., Piterman, N., Pnueli, A., Zuck, L.: Liveness with invisible ranking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 223–238. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24622-0_19CrossRefGoogle Scholar
  21. 21.
  22. 22.
    Fey, G., Staber, S., Bloem, R., Drechsler, R.: Automatic fault localization for property checking. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 27, 1138–1149 (2008)CrossRefGoogle Scholar
  23. 23.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-36387-4CrossRefzbMATHGoogle Scholar
  24. 24.
    Habermehl, P., Vojnar, T.: Regular model checking using inference of regular languages. In: Bradfield, J.C., Moller, F. (eds.) Proceedings of the 6th International Workshop on Verification of Infinite-State Systems, INFINITY 2004 (2004)Google Scholar
  25. 25.
    Jobstmann, B., Griesmayer, A., Bloem, R.: Program repair as a game. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 226–238. Springer, Heidelberg (2005).  https://doi.org/10.1007/11513988_23CrossRefGoogle Scholar
  26. 26.
    Katis, A., et al.: Validity-guided synthesis of reactive systems from assume-guarantee contracts. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 176–193. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-89963-3_10CrossRefGoogle Scholar
  27. 27.
    Kearns, M.J., Vazirani, U.: An Introduction to Computational Learning Theory. MIT Press, Cambridge (2014)Google Scholar
  28. 28.
    Kesten, Y., Maler, O., Marcus, M., Pnueli, A., Shahar, E.: Symbolic model checking with rich assertional languages. TCS 256(1–2), 93–112 (2001)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Lin, A.W., Rümmer, P.: Liveness of randomised parameterised systems under arbitrary schedulers. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 112–133. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-41540-6_7CrossRefGoogle Scholar
  30. 30.
    McNaughton, R.: Infinite games played on finite graphs. Ann. Pure Appl. Logic 65(2), 149–184 (1993)MathSciNetCrossRefGoogle Scholar
  31. 31.
    de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78800-3_24CrossRefGoogle Scholar
  32. 32.
    Neider, D.: Small strategies for safety games. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 306–320. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-24372-1_22CrossRefzbMATHGoogle Scholar
  33. 33.
    Neider, D., Jansen, N.: Regular model checking using solver technologies and automata learning. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 16–31. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38088-4_2CrossRefGoogle Scholar
  34. 34.
    Neider, D., Markgraf, O.: Learning-based synthesis of safety controllers. In: Formal Methods in Computer Aided Design, FMCAD 2019, San Jose, CA, USA, 22–25 October 2019. pp. 120–128 (2019)Google Scholar
  35. 35.
    Neider, D., Topcu, U.: An automaton learning approach to solving safety games over infinite graphs. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 204–221. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49674-9_12CrossRefGoogle Scholar
  36. 36.
    Nerode, A.: Linear automaton transformations. Proc. Am. Math. Soc. 9(4), 541–544 (1958)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Oncina, J., Garcia, P.: Inferring regular languages in polynomial updated time. In: Pattern Recognition and Image Analysis: Selected Papers from the IVth Spanish Symposium, pp. 49–61. World Scientific (1992)Google Scholar
  38. 38.
    Pnueli, A., Shahar, E.: Liveness and acceleration in parameterized verification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 328–343. Springer, Heidelberg (2000).  https://doi.org/10.1007/10722167_26CrossRefzbMATHGoogle Scholar
  39. 39.
    Rivest, R.L., Schapire, R.E.: Inference of finite automata using homing sequences. Inf. Comput. 103(2), 299–347 (1993)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Solar-Lezama, A.: The sketching approach to program synthesis. In: Hu, Z. (ed.) APLAS 2009. LNCS, vol. 5904, pp. 4–13. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-10672-9_3CrossRefGoogle Scholar
  41. 41.
    Solar-Lezama, A., Arnold, G., Tancau, L., Bodík, R., Saraswat, V.A., Seshia, S.A.: Sketching stencils. ACM (2007)Google Scholar
  42. 42.
    Solar-Lezama, A., Tancau, L., Bodík, R., Seshia, S.A., Saraswat, V.A.: Combinatorial sketching for finite programs (2006)Google Scholar
  43. 43.
    Staber, S., Bloem, R.: Fault localization and correction with QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 355–368. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-72788-0_34CrossRefzbMATHGoogle Scholar
  44. 44.
    Tomlin, C.J., Lygeros, J., Sastry, S.S.: A game theoretic approach to controller design for hybrid systems. Proc. IEEE 88, 949–970 (2000)CrossRefGoogle Scholar
  45. 45.
    Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Using language inference to verify omega-regular properties. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 45–60. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31980-1_4CrossRefGoogle Scholar
  46. 46.
    Vardhan, A., Viswanathan, M.: LEVER: a tool for learning based verification. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 471–474. Springer, Heidelberg (2006).  https://doi.org/10.1007/11817963_43CrossRefGoogle Scholar
  47. 47.
    Vojnar, T.: Cut-offs and automata in formal verification of infinite-state systems, : habilitation Thesis. Brno University of Technology, Faculty of Information Technology (2007)Google Scholar
  48. 48.
    Vojnar, T.: Cut-offs and Automata in Formal Verification of Infinite-State Systems. FIT Monograph 1, Faculty of Information Technology BUT (2007)Google Scholar
  49. 49.
    Zuck, L.D., Pnueli, A.: Model checking and abstraction to the aid of parameterized systems (a survey). Comput. Lang. Syst. Struct. 30, 139–169 (2004)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Oliver Markgraf
    • 1
    Email author
  • Chih-Duo Hong
    • 3
  • Anthony W. Lin
    • 1
    • 2
  • Muhammad Najib
    • 1
  • Daniel Neider
    • 2
  1. 1.Technical University of KaiserslauternKaiserslauternGermany
  2. 2.Max Planck Institute for Software SystemsKaiserslauternGermany
  3. 3.University of OxfordOxfordEngland

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