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Mechanically Proving Determinacy of Hierarchical Block Diagram Translations

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11388))

Abstract

Hierarchical block diagrams (HBDs) are at the heart of embedded system design tools, including Simulink. Numerous translations exist from HBDs into languages with formal semantics, amenable to formal verification. However, none of these translations has been proven correct, to our knowledge.

We present in this paper the first mechanically proven HBD translation algorithm. The algorithm translates HBDs into an algebra of terms with three basic composition operations (serial, parallel, and feedback). In order to capture various translation strategies resulting in different terms achieving different tradeoffs, the algorithm is nondeterministic. Despite this, we prove its semantic determinacy: for every input HBD, all possible terms that can be generated by the algorithm are semantically equivalent. We apply this result to show how three Simulink translation strategies introduced previously can be formalized as determinizations of the algorithm, and derive that these strategies yield semantically equivalent results (a question left open in previous work). All results are formalized and proved in the Isabelle theorem-prover and the code is publicly available.

This work has been partially supported by the Academy of Finland and the U.S. National Science Foundation (awards #1329759 and #1801546). V. Preoteasa—Partially supported by the ECSEL JU MegaM@Rt2 project under grant agreement #737494. I. Dragomir—Partially supported by the the European Union’s Horizon 2020 research and innovation programme under grant agreement #730080 (ESROCOS).

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References

  1. Rahim, L.A., Whittle, J.: A survey of approaches for verifying model transformations. Softw. Syst. Model. 14(2), 1003–1028 (2015)

    Article  Google Scholar 

  2. Agrawal, A., Simon, G., Karsai, G.: Semantic translation of Simulink/stateflow models to hybrid automata using graph transformations. Electron. Notes Theor. Comput. Sci. 109, 43–56 (2004)

    Article  Google Scholar 

  3. Amrani, M., et al.: Formal verification techniques for model transformations: a tridimensional classification. J. Object Technol. 14(3), 1:1–43 (2015)

    Article  Google Scholar 

  4. Auger, C.: Compilation certifiée de SCADE/LUSTRE. (Certified compilation of SCADE/LUSTRE). Ph.D. thesis, University of Paris-Sud, Orsay, France (2013). (in French)

    Google Scholar 

  5. Back, R.-J., von Wright, J.: Refinement Calculus: A Systematic Introduction. Springer, New York (1998). https://doi.org/10.1007/978-1-4612-1674-2

    Book  MATH  Google Scholar 

  6. Baez, J.C., Erbele, J.: Categories in control. CoRR, abs/1405.6881 (2015)

    Google Scholar 

  7. Ballarin, C.: Locales: a module system for mathematical theories. J. Autom. Reason. 52(2), 123–153 (2014)

    Article  MathSciNet  Google Scholar 

  8. Berry, G.: The constructive semantics of pure Esterel (1999)

    Google Scholar 

  9. Bouissou, O., Chapoutot, A.: An operational semantics for Simulink’s simulation engine. SIGPLAN Not. 47(5), 129–138 (2012)

    Google Scholar 

  10. Bourke, T., Brun, L., Dagand, P.É., Leroy, X., Pouzet, M., Rieg, L.: A formally verified compiler for lustre. SIGPLAN Not. 52(6), 586–601 (2017)

    Article  Google Scholar 

  11. Calegari, D., Szasz, N.: Verification of model transformations. Electron. Notes Theor. Comput. Sci. 292, 5–25 (2013)

    Article  Google Scholar 

  12. Chen, C., Dong, J.S., Sun, J.: A formal framework for modeling and validating Simulink diagrams. Form. Asp. Comput. 21(5), 451–483 (2009)

    Article  Google Scholar 

  13. Courcelle, B.: A representation of graphs by algebraic expressions and its use for graph rewriting systems. In: Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds.) Graph Grammars 1986. LNCS, vol. 291, pp. 112–132. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-18771-5_49

    Chapter  Google Scholar 

  14. Ştefănescu, G.: Network Algebra. Springer, London (2000). https://doi.org/10.1007/978-1-4471-0479-7

    Book  MATH  Google Scholar 

  15. Dijkstra, E.W.: Guarded commands, nondeterminacy and formal derivation of programs. Commun. ACM 18(8), 453–457 (1975)

    Article  MathSciNet  Google Scholar 

  16. Dragomir, I., Preoteasa, V., Tripakis, S.: Compositional semantics and analysis of hierarchical block diagrams. In: Bošnački, D., Wijs, A. (eds.) SPIN 2016. LNCS, vol. 9641, pp. 38–56. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32582-8_3

    Chapter  Google Scholar 

  17. Dragomir, I., Preoteasa, V., Tripakis, S.: The refinement calculus of reactive systems toolset. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 201–208. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_12

    Chapter  Google Scholar 

  18. Dragomir, I., Preoteasa, V., Tripakis, S.: The refinement calculus of reactive systems toolset - February 2018. Figshare. https://doi.org/10.6084/m9.figshare.5900911. Accessed Feb 2018

  19. Eclipse: ATL - a model transformation technology. http://www.eclipse.org/atl/

  20. Edwards, S., Lee, E.A.: The semantics and execution of a synchronous block-diagram language. Sci. Comput. Prog. 48, 21–42(22) (2003)

    Article  MathSciNet  Google Scholar 

  21. Ghica, D.R., Jung, A.: Categorical semantics of digital circuits. In: Piskac, R., Talupur, M. (eds.) 2016 Formal Methods in Computer-Aided Design, FMCAD 2016, Mountain View, CA, USA, 3–6 October 2016, pp. 41–48. IEEE (2016)

    Google Scholar 

  22. Ghica, D.R., Jung, A., Lopez, A.: Diagrammatic semantics for digital circuits. In: Goranko, V., Dam, M. (eds.) 26th EACSL Annual Conference on Computer Science Logic, CSL 2017, LIPIcs, Stockholm, Sweden, vol. 82, pp. 24:1–24:16. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)

    Google Scholar 

  23. Ghica, D.R., Lopez, A.: A structural and nominal syntax for diagrams. In: Coecke, B., Kissinger, A. (eds.) Proceedings 14th International Conference on Quantum Physics and Logic, QPL 2017, EPTCS, Nijmegen, The Netherlands, 3–7 July 2017, vol. 266, pp. 71–83 (2017)

    Article  MathSciNet  Google Scholar 

  24. Yang, C., Vyatkin, V.: Transformation of Simulink models to IEC 61499 function blocks for verification of distributed control systems. Control Eng. Pract. 20(12), 1259–1269 (2012)

    Article  Google Scholar 

  25. Leroy, X., Blazy, S., Kästner, D., Schommer, B., Pister, M., Ferdinand, C.: CompCert - a formally verified optimizing compiler. In: 8th European Congress on ERTS 2016: Embedded Real Time Software and Systems, Toulouse, France, January 2016. SEE

    Google Scholar 

  26. Lúcio, L., et al.: Model transformation intents and their properties. Softw. Syst. Model. 15(3), 647–684 (2016)

    Article  Google Scholar 

  27. Malik, S.: Analysis of cyclic combinational circuits. IEEE Trans. Comput.-Aided Des. 13(7), 950–956 (1994)

    Article  Google Scholar 

  28. MathWorks: Simulink. https://www.mathworks.com/products/simulink.html

  29. Meenakshi, B., Bhatnagar, A., Roy, S.: Tool for translating Simulink models into input language of a model checker. In: Liu, Z., He, J. (eds.) ICFEM 2006. LNCS, vol. 4260, pp. 606–620. Springer, Heidelberg (2006). https://doi.org/10.1007/11901433_33

    Chapter  Google Scholar 

  30. Minopoli, S., Frehse, G.: SL2SX translator: from Simulink to SpaceEx models. In: Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016, pp. 93–98. ACM, New York (2016)

    Google Scholar 

  31. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL – A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45949-9

    Book  MATH  Google Scholar 

  32. Preoteasa, V., Dragomir, I., Tripakis, S.: Mechanically proving determinacy of hierarchical block diagram translations. CoRR, abs/1611.01337 (2018)

    Google Scholar 

  33. Preoteasa, V., Tripakis, S.: Towards compositional feedback in non-deterministic and non-input-receptive systems. In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, pp. 768–777. ACM, New York (2016)

    Google Scholar 

  34. Reicherdt, R., Glesner, S.: Formal verification of discrete-time MATLAB/Simulink models using Boogie. In: Giannakopoulou, D., Salaün, G. (eds.) SEFM 2014. LNCS, vol. 8702, pp. 190–204. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10431-7_14

    Chapter  Google Scholar 

  35. Ryabtsev, M., Strichman, O.: Translation validation: from Simulink to C. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 696–701. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02658-4_57

    Chapter  Google Scholar 

  36. Schlesinger, S., Herber, P., Göthel, T., Glesner, S.: Proving transformation correctness of refactorings for discrete and continuous Simulink models. In: ICONS 2016, The Eleventh International Conference on Systems, EMBEDDED 2016, International Symposium on Advances in Embedded Systems and Applications, pp. 45–50. IARIA XPS Press (2016)

    Google Scholar 

  37. Schmeck, H.: Algebraic characterization of reducible flowcharts. J. Comput. Syst. Sci. 27(2), 165–199 (1983)

    Article  MathSciNet  Google Scholar 

  38. Selinger, P.: A survey of graphical languages for Monoidal categories. In: Coecke, B. (ed.) New Structures for Physics. LNP, vol. 813, pp. 289–355. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-12821-9_4

    Chapter  MATH  Google Scholar 

  39. Sfyrla, V., Tsiligiannis, G., Safaka, I., Bozga, M., Sifakis, J.: Compositional translation of Simulink models into synchronous BIP. In: SIES, pp. 217–220, July 2010

    Google Scholar 

  40. The Coq Development Team: The Coq proof assistant reference. INRIA, 2016. Version 8.5 (2016)

    Google Scholar 

  41. Tripakis, S., Sofronis, C., Caspi, P., Curic, A.: Translating discrete-time Simulink to Lustre. ACM Trans. Embed. Comput. Syst. 4(4), 779–818 (2005)

    Article  Google Scholar 

  42. Zanasi, F.: Interacting Hopf algebras - the theory of linear systems. (Interacting Hopf Algebras - la théorie des systèmes linéaires). Ph.D. thesis, École normale supérieure de Lyon, France (2015)

    Google Scholar 

  43. Zhou, C., Kumar, R.: Semantic translation of Simulink diagrams to input/output extended finite automata. Discret. Event Dyn. Syst. 22(2), 223–247 (2012)

    Article  MathSciNet  Google Scholar 

  44. Zou, L., Zhany, N., Wang, S., Franzle, M., Qin, S.: Verifying Simulink diagrams via a hybrid Hoare logic prover. In: EMSOFT, pp. 9:1–9:10, September 2013

    Google Scholar 

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Acknowledgments

We would like to thank Gheorghe Ştefănescu for his help with the algebra of flownomials.

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Authors and Affiliations

  1. Space Systems Finland, Espoo, Finland

    Viorel Preoteasa

  2. Univ. Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), VERIMAG, 38000, Grenoble, France

    Iulia Dragomir

  3. Aalto University, Espoo, Finland

    Viorel Preoteasa & Stavros Tripakis

  4. Northeastern University, Boston, USA

    Stavros Tripakis

Authors
  1. Viorel Preoteasa
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  2. Iulia Dragomir
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  3. Stavros Tripakis
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Corresponding authors

Correspondence to Viorel Preoteasa , Iulia Dragomir or Stavros Tripakis .

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Editors and Affiliations

  1. IRIF, University Paris Diderot and CNRS, Paris, France

    Constantin Enea

  2. Yale University, New Haven, CT, USA

    Ruzica Piskac

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Preoteasa, V., Dragomir, I., Tripakis, S. (2019). Mechanically Proving Determinacy of Hierarchical Block Diagram Translations. In: Enea, C., Piskac, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2019. Lecture Notes in Computer Science(), vol 11388. Springer, Cham. https://doi.org/10.1007/978-3-030-11245-5_27

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  • DOI: https://doi.org/10.1007/978-3-030-11245-5_27

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