A formal verification technique for behavioural model-to-model transformations

Abstract

In Model Driven Software Engineering, models and model transformations are the primary artifacts when developing a software system. In such a workflow, model transformations are used to incrementally transform initial abstract models into concrete models containing all relevant system details. Over the years, various formal methods have been proposed and further developed to determine the functional correctness of models of concurrent systems. However, the formal verification of model transformations has so far not received as much attention. In this article, we propose a formal verification technique to determine that formalisations of such transformations in the form of rule systems are guaranteed to preserve functional properties, regardless of the models they are applied on. This work extends our earlier work in various ways. Compared to our earlier approaches, the current technique involves only up to n individual checks, with n the number of rules in the rule system, whereas previously, up to 2n − 1 checks were required. Furthermore, a full correctness proof for the technique is presented, based on a formal proof conducted with the Coq proof assistant. Finally, we report on two sets of conducted experiments. In the first set, we compared traditional model checking with transformation verification, and in the second set, we compared the verification technique presented in this article with the previous version.

References

  1. ABH+10

    Abrial J-R, Butler M, Hallerstede S, Hoang TS, Mehta F, Voisin L (2010) Rodin: an open toolset for modelling and reasoning in Event-B. Softw Tools Technol Transf 12(6): 447–466

    Article  Google Scholar 

  2. ACL+15

    Amrani M, Combemale B, Lúcio L, Selim GMK, Dingel J, Le Traon Y, Vangheluwe H, Cordy JR (2015) Formal verification techniques for model transformations: a tridimensional classification. J Object Technol 14(3): 1–43

    Article  Google Scholar 

  3. AL91

    Abadi M, Lamport L (1991) The existence of refinement mappings. Theor Comput Sci 82: 253–284

    MathSciNet  Article  MATH  Google Scholar 

  4. BCE+07

    Baldan P, Corradini A, Ehrig H, Heckel R, König B (2007) Bisimilarity and behaviour-preserving reconfigurations of open petri nets. In: Proceeding of 2nd conference on algebra and coalgebra in computer science (CALCO 2007), volume 4624 of LNCS. Springer, pp 126–142

  5. BE04

    Braunstein C, Encrenaz E (2004) CTL-property transformation along an incremental design process. In: Proceeding of 4th international workshop on automated verification of critical systems, volume 128 of ENTCS. Elsevier, pp 263–278

  6. BEdL+16

    Bal H, Epema D, de Laat C, van Nieuwpoort R, Romein J, Seinstra F, Snoek C, Wijshoff H (216) A medium-scale distributed system for computer science research: infrastructure for the long term. IEEE Comput 49(5): 54–63

  7. BESW10

    Bošnački D, Edelkamp S, Sulewski D, Wijs AJ (2010) GPU-PRISM: an extension of PRISM for general purpose graphics processing units. In: Proceeding of 9th international workshop on parallel and distributed methods in verification (PDMC 2010). IEEE Computer Society Press, pp 17–19

  8. BGL05

    Blech JO, Glesner S, Leitner J (2005) Formal verification of java code generation from UML models. In: 3rd international fujaba days. Fujaba Days, pp 49–56

  9. BH04

    Bowen JP, Hinchey MG (2004) Formal methods. In: Computldbook, chapter 106. ACM, pp 106–1–106–25

  10. BK08

    Baier C, Katoen J-P (2008) Principles of model checking. MIT Press, Cambridge

    MATH  Google Scholar 

  11. CCGT09

    Combemale B, Crégut X, Garoche P-L, Thirioux X (2009) Essay on semantics definition in MDE: an instrumented approach for model verification. J Softw 4(9): 943–958

    Article  Google Scholar 

  12. CGK+13

    Cranen S, Groote JF, Keiren JJA, Stappers FPM, de Vink EP, Wesselink W, Willemse T (2013) An overview of the mCRL2 toolset and its recent advances. In: Proceeding of 19th international conference on tools and algorithms for the construction and analysis of systems (TACAS 2013), volume 7795 of LNCS. Springer, pp 199–213

  13. DP06

    Dodds M, Plump D (2006) Graph transformation in constant time. In: Proceeding of 3rd international conference on graph transformation (ICGT 2006), volume 4178 of LNCS. Springer, pp 367–382

  14. EGI97

    Eppstein D, Galil Z, Italiano G (1997) Dynamic graph algorithms. In: CRC handbook of algorithms and theory of computation chapter 22. CRC Press, Boca Raton

  15. FPW05

    Fokkink WJ, Pang J, Wijs AJ (2005) Is timed branching bisimilarity an equivalence indeed? In: Proceeding of 3rd conference on formal modelling and analysis of timed systems (FORMATS 2005), volume 3829 of Lecture Notes in Computer Science. Springer, pp 258–272

  16. GGL+06

    Giese H, Glesner S, Leitner J, Schäfer W, Wagner R (2006) Towards verified model transformations. In: Proceeding of 3rd workshop on model-driven engineering, verification, and validation (MoDeVVa 2006), pp 78–93

  17. GL12

    Giese H, Lambers L (2012) Towards automatic verification of behavior preservation for model transformation via invariant checking. In: Proceeding of 6th international conference on graph transformation (ICGT 2012), volume 7562 of LNCS. Springer, pp 249–263

  18. GLMS11

    Garavel H, Lang F, Mateescu R, Serwe W (2011) CADP 2010: A toolbox for the construction and analysis of distributed processes. In: Proceeding of 17th international conference on tools and algorithms for the construction and analysis of systems (TACAS 2011), volume 6605 of LNCS. Springer, pp 372–387

  19. GS99

    Garavel H, Sighireanu M (1999) A graphical parallel composition operator for process algebras. In: Proceeding of 1999 IFIP TC6/WG6.1 joint international conference on formal description techniques and protocol specification, testing and verification (FORTE/PSTV 1999), volume 156 of IFIP conference proceedings. Kluwer, pp 185–202

  20. GW16

    Groote JF, Wijs AJ (2016) An \({O(m \log n)}\) algorithm for stuttering equivalence and branching bisimulation. In: Proceeding of 22nd international conference on tools and algorithms for the construction and analysis of systems (TACAS 2016), volume 9636 of LNCS. Springer, pp 607–624

  21. HKR+10

    Hülsbusch M, König B, Rensink A,Semenyak M, Soltenborn C, Wehrheim H (2010) Showing full semantics preservation in model transformations: a comparison of techniques. In: Proceeding of 8th international conference on integrated formal methods (iFM 2010), volume 6396 of LNCS, pp 183–198. Springer.

  22. KLG07

    Kundu S, Lerner S, Gupta R (2007) Automated refinement checking of concurrent systems. In: Proceeding of 26th international conference on computer-aided design (ICCAD 2007). IEEE, pp 318–325

  23. KN07

    Karsai G, Narayanan A (2007) On the correctness of model transformations in the development of embedded systems. In: Proceeding of 13th monterey workshop 2006, volume 4888 of LNCS. Springer, pp 1–18

  24. KNP11

    Kwiatkowska M, Norman G, Parker D (2011) PRISM 4.0: verification of probabilistic real-time systems. In: Proceeding of 23rd international conference on computer aided verification (CAV 2011), volume 6806 of LNCS. Springer, pp 585–591

  25. KR08

    Kahsai T, Roggenbach M (2008) Property preserving refinement for Csp-Casl. In: Proceeding of 19th international workshop on algebraic development techniques (WADT 2008), volume 5486 of LNCS. Springer, pp 206–220

  26. KWB05

    Kleppe A, Warmer J, Bast W (2005) MDA Explained: The Model Driven Architecture(TM): Practice and Promise. Addison-Wesley Professional

  27. Lan96

    Lano K (1996) The B language and method, a guide to practical formal development. Springer, New York

    Google Scholar 

  28. Lan06

    Lang F (2006) Refined interfaces for compositional verification. In: Proceeding of 26th international conference on formal methods for networked and distributed systems (FORTE 2006), volume 4229 of LNCS. Springer, pp 159–174

  29. LM13

    Lang F, Mateescu R (2013) Partial model checking using networks of labelled transition systems and boolean equation systems. Log Methods Comput Sci 9(4): 1–32

    MathSciNet  MATH  Google Scholar 

  30. Lut97

    Luttik SP (1997) Description and formal specification of the link layer of P1394. Technical Report SEN-R9706, CWI

  31. MW14

    Mateescu R, Wijs AJ (2014) Property-dependent reductions adequate with divergence-sensitive branching bisimilarity. Sci Comput Program 96(3): 354–376

    Article  Google Scholar 

  32. Nat99

    National Institute of Standards and Technology (1999) Data encryption standard (DES). Federal information processing standards pp 46–3

  33. NK08

    Narayanan A, Karsai G (2008) Towards verifying model transformations. In: Proceeding of 7th international workshop on graph transformation and visual modeling techniques (GT-VMT 2008), volume 211 of ENTCS. Elsevier, pp 191–200

  34. Plo09

    Ploeger B (2009) Analysis of ACS using mCRL2. Technical Report 09-11, Eindhoven University of Technology

  35. PW16

    de Putter S, Wijs AJ (2016) Verifying a verifier: on the formal correctness of an LTS transformation verification technique. In: Proceeding of 19th international conference on fundamental approaches to software engineering (FASE 2016), volume 9633 of LNCS. Springer, pp 383–400

  36. Rom99

    Romijn J (1999) Model checking a HAVi leader election protocol. Technical Report SEN-R9915, CWI

  37. RR96

    Ramalingam G, Reps T (1996) On the computational complexity of dynamic graph problems. Theor Comput Sci 158: 233–277

    MathSciNet  Article  MATH  Google Scholar 

  38. RW13

    Rahim LA, Whittle J (2013) A survey of approaches for verifying model transformations. Softw Syst Model pp 1–26.

  39. Sah07

    Saha D (2007) An incremental bisimulation algorithm. In: Proceeding of 27th iarcs annual conference on foundations of software technology and theoretical computer science (FSTTCS 2007), volume 4855 of LNCS. Springer, pp 204–215

  40. SLC+14

    Selim GMK, Lúcio L, Cordy JR, Dingel J, Oakes BJ (2014) Specification and verification of graph-based model transformation properties. In: Proceeding of 9th international colloquium on graph theory and combinatorics (ICGT 2014), volume 8571 of LNCS. Springer, pp 113–129

  41. SMR11

    Stenzel K, Moebius N, Reif W (2011) Formal verification of QVT transformations for code generation. In: Proceeding of 14th international conference on model driven engineering languages and systems (MODELS 2011), volume 6981 of LNCS. Springer, pp 533–547

  42. SS94

    Sokolsky OV, Smolka SA (1994) Incremental model checking in the modal Mu-Calculus. In: Proceeding of 6th international conference on computer aided verification (CAV 1994), volume 818 of LNCS. Springer, pp 351–363

  43. Swa96

    Swamy GM (1996) Incremental methods for formal verification and logic synthesis. PhD thesis, University of California

  44. vGW96

    van Glabbeek RJ, Weijland WP (1996) Branching time and abstraction in bisimulation semantics. J ACM 43(3): 555–600

    MathSciNet  Article  MATH  Google Scholar 

  45. VP03

    Varró D, Pataricza A (2003) Automated formal verification of model transformations. In: Proceeding of 2nd international workshop on critical systems development with UML (CSDUML 2003), pp 63–78

  46. WE13

    Wijs AJ, Engelen LJP (2013) Efficient property preservation checking of model refinements. In: Proceeding of 19th international conference on tools and algorithms for the construction and analysis of systems (TACAS 2013), volume 7795 of LNCS. Springer, pp 565–579

  47. WE14

    Wijs AJ, Engelen LJP (2014) Refiner: towards formal verification of model transformations. In: Proceeding of 6th NASA formal methods symposium (NFM 2014), volume 8430 of LNCS. Springer, pp 258–263

  48. WF05

    Wijs AJ, Fokkink WJ (2005) From \({\chi_{\textnormal{t}}}\) to \({\mu}\) CRL: combining performance and functional analysis. In: Proceeding of 10th conference on engineering of complex computer systems (ICECCS 2005). IEEE Computer Society Press, pp 184–193

  49. Wij07

    Wijs AJ (2007) Achieving discrete relative timing with untimed process algebra. In: Proceeding of 12th conference on engineering of complex computer systems (ICECCS 2007). IEEE Computer Society Press, pp 35–44

  50. Wij13

    Wijs AJ (2013) Define, verify, refine: correct composition and transformation of concurrent system semantics. In: Proceeding of 10th international symposium on formal aspects of component software (FACS 2013), volume 8348 of LNCS. Springer, pp 348–368

  51. Wij15

    Wijs AJ (2015) Confluence detection for transformations of labelled transition systems. In: Proceeding of 2nd graphs as models workshop (GaM 2015), volume 181 of EPTCS. Open Publishing Association, pp 1–15

  52. Win90

    Winskel G (1990) A compositional proof system on a category of labelled transition systems. Inf Comput 87(1-2): 2–57

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Sander de Putter or Anton Wijs.

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Perdita Stevens, Andrzej Wasowski, and Ewen Denney

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de Putter, S., Wijs, A. A formal verification technique for behavioural model-to-model transformations. Form Asp Comp 30, 3–43 (2018). https://doi.org/10.1007/s00165-017-0437-z

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Keywords

  • Model transformation verification
  • Explicit-state model checking
  • Branching bisimulation