Skip to main content
SpringerLink
Log in

Proving Local Invariants in ASTDs

  • Conference paper
  • First Online:
Formal Methods and Software Engineering (ICFEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14308))

Included in the following conference series:

  • 231 Accesses

Abstract

This paper proposes a formal approach for generating proof obligations to verify local invariants in an Algebraic State Transition Diagram (ASTD). ASTD is a graphical specification language that allows for the combination of extended hierarchical state machines using CSP-like process algebra operators. Invariants can be declared at any level in a specification (state, ASTD), fostering the decomposition of system invariants into modular local invariants which are easier to prove, because proof obligations are smaller. The proof obligations take advantage of the structure of an ASTD to use local invariants as hypotheses. ASTD operators covered are automaton, sequence, closure and guard. Proof obligations are discharged using Rodin. When proof obligations cannot be proved, ProB can be used to identify counter-examples to help in correcting/reinforcing the invariant or the specification.

This work was supported by the ANR projet DISCONT, Public Safety Canada and NSERC.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://www.event-b.org/.

References

  1. de Azevedo Oliveira, D., Frappier, M.: Modelling an automotive software system with TASTD. In: Glässer, U., Creissac Campos, J., Méry, D., Palanque, P. (eds.) Rigorous State-Based Methods (ABZ2023). LNCS, vol. 14010, pp. 124–141. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-33163-3_10

  2. de Azevedo Oliveira, D., Frappier, M.: TASTD: A real-time extension for ASTD. In: Glässer, U., Campos, J.C., Méry, D., Palanque, P.A. (eds.) Rigorous State-Based Methods (ABZ2023). LNCS, vol. 14010, pp. 142–159. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-33163-3_11

  3. Cartellier, Q.: https://gitlab.com/QCartellier/icfem2023-poastd/-/tree/main/ (2023)

  4. El Jabri, C., Frappier, M., Ecarot, T., Tardif, P.M.: Development of monitoring systems for anomaly detection using ASTD specifications. In: Aït-Ameur, Y., Crăciun, F. (eds.) TASE. LNCS, vol. 13299, pp. 274–289. Springer (2022). https://doi.org/10.1007/978-3-031-10363-6_19

  5. Fayolle, T.: Combinaison de méthodes formelles pour la spécification de systèmes industriels. Theses, Université Paris-Est; Université de Sherbrooke, Québec, Canada, June 2017

    Google Scholar 

  6. Frappier, M., Gervais, F., Laleau, R., Fraikin, B., St-Denis, R.: Extending Statecharts with process algebra operators. ISSE 4(3), 285–292 (2008)

    Google Scholar 

  7. Khan, A.H., Rauf, I., Porres, I.: Consistency of UML class and Statechart diagrams with state invariants. In: MODELSWARD, pp. 14–24. SciTePress (2013)

    Google Scholar 

  8. Leuschel, M., Butler, M.: ProB: an automated analysis toolset for the B Method. JSTTT 10(2), 185–203 (2008)

    Google Scholar 

  9. Mammar, A., Frappier, M.: Modeling of a speed control system using event-B. In: Raschke, A., Méry, D., Houdek, F. (eds.) ABZ 2020. LNCS, vol. 12071, pp. 367–381. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48077-6_29

    Chapter  Google Scholar 

  10. Mammar, A., Frappier, M., Laleau, R.: An event-B model of an automotive adaptive exterior light system. In: Raschke, A., Méry, D., Houdek, F. (eds.) ABZ 2020. LNCS, vol. 12071, pp. 351–366. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48077-6_28

    Chapter  Google Scholar 

  11. Milhau, J., Frappier, M., Gervais, F., Laleau, R.: Systematic translation rules from ASTD to event-B. In: Méry, D., Merz, S. (eds.) IFM 2010. LNCS, vol. 6396, pp. 245–259. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16265-7_18

    Chapter  Google Scholar 

  12. Nganyewou Tidjon, L., Frappier, M., Leuschel, M., Mammar, A.: Extended algebraic state-transition diagrams. In: 2018 23rd International Conference on Engineering of Complex Computer Systems (ICECCS), pp. 146–155. IEEE Computer Society (2018)

    Google Scholar 

  13. Porres, I., Rauf, I.: Generating class contracts from UML protocol statemachines. In: Proceedings of the 6th International Workshop on Model-Driven Engineering, Verification and Validation. MoDeVVa 2009, ACM, New York, USA (2009)

    Google Scholar 

  14. Porres, I., Rauf, I.: From nondeterministic UML protocol statemachines to class contracts. In: 2010 Third International Conference on Software Testing, Verification and Validation, pp. 107–116 (2010)

    Google Scholar 

  15. Riviere, P., Singh, N.K., Ameur, Y.A., Dupont, G.: Formalising liveness properties in event-b with the reflexive EB4EB framework. In: Rozier, K.Y., Chaudhuri, S. (eds.) NASA Formal Methods - 15th International Symposium, NFM 2023, Houston, TX, USA, May 16–18, 2023, Proceedings. Lecture Notes in Computer Science, vol. 13903, pp. 312–331. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-33170-1_19

  16. Said, M.Y., Butler, M.J., Snook, C.F.: A method of refinement in UML-B. Softw. Syst. Model. 14(4), 1557–1580 (2015)

    Article  Google Scholar 

  17. Sekerinski, E.: Verifying Statecharts with state invariants. In: 13th International Conference on Engineering of Complex Computer Systems (ICECCS), pp. 7–14. IEEE Computer Society (2008)

    Google Scholar 

  18. Tidjon, L.N., Frappier, M., Mammar, A.: Intrusion detection using ASTDs. In: Barolli, L., Amato, F., Moscato, F., Enokido, T., Takizawa, M. (eds.) AINA 2020. AISC, vol. 1151, pp. 1397–1411. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44041-1_118

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GRIC, Université de Sherbrooke, Sherbrooke, J1K2R1, QC, Canada

    Quelen Cartellier & Marc Frappier

  2. SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, 91120, Palaiseau, France

    Amel Mammar

Authors
  1. Quelen Cartellier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marc Frappier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amel Mammar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Quelen Cartellier .

Editor information

Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Yi Li

  2. Concordia University, Montreal, QC, Canada

    Sofiène Tahar

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cartellier, Q., Frappier, M., Mammar, A. (2023). Proving Local Invariants in ASTDs. In: Li, Y., Tahar, S. (eds) Formal Methods and Software Engineering. ICFEM 2023. Lecture Notes in Computer Science, vol 14308. Springer, Singapore. https://doi.org/10.1007/978-981-99-7584-6_14

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-7584-6_14

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-7583-9

  • Online ISBN: 978-981-99-7584-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation