Advertisement

Formal Methods in System Design

, Volume 41, Issue 2, pp 211–231 | Cite as

Probabilistic contracts for component-based design

  • Gregor Gössler
  • Dana N. Xu
  • Alain Girault
Article

Abstract

We define a framework of probabilistic contracts for constructing component-based embedded systems, based on the formalism of discrete-time Interactive Markov Chains. A contract specifies the assumptions a component makes on its context and the guarantees it provides. Probabilistic transitions represent allowed uncertainty in the component behavior, for instance, to model internal choice or reliability. Action transitions are used to model non-deterministic behavior and communication between components. An interaction model specifies how components interact with each other.

We provide the ingredients for a component-based design flow, including (1) contract satisfaction and refinement, (2) parallel composition of contracts over disjoint, interacting components, and (3) conjunction of contracts describing different requirements over the same component. Compositional design is enabled by congruence of refinement.

Keywords

Component Probabilistic contract Refinement Composition 

References

  1. 1.
    Aho AV, Sethi R, Ullman JD (1986) Compilers—principles, techniques, and tools. Addison-Wesley, Reading Google Scholar
  2. 2.
    Caillaud B, Delahaye B, Larsen KG, Legay A, Pedersen ML, Wasowski A (2010) Compositional design methodology with constraint Markov chains. In: International conference on the quantitative evaluation of systems, QEST’10, pp 123–132 Google Scholar
  3. 3.
    de Alfaro L, Henzinger TA, Jhala R (2001) Compositional methods for probabilistic systems. In: Larsen KG, Nielsen M (eds) Proc CONCUR 2001—concurrency theory, 12th international conference. LNCS, vol 2154. Springer, Berlin, pp 351–365 Google Scholar
  4. 4.
    Delahaye B, Caillaud B, Legay A (2011) Probabilistic contracts: a compositional reasoning methodology for the design of systems with stochastic and/or non-deterministic aspects. Form Methods Syst Des 38(1):1–32 zbMATHCrossRefGoogle Scholar
  5. 5.
    Doyen L, Petrov T, Henzinger TA, Jobstmann B (2008) Interface theories with component reuse. In: International conference on embedded software, EMSOFT’08. ACM, New York, pp 79–88 Google Scholar
  6. 6.
    Fecher H, Leucker M, Wolf V (2006) Don’t know in probabilistic systems. In: International workshop on model checking software, SPIN’06. LNCS, vol 3925. Springer, Berlin, pp 71–88 CrossRefGoogle Scholar
  7. 7.
    Gössler G, Raclet J-B (2009) Modal contracts for component-based design. In: International conference on software engineering and formal methods, SEFM’09. IEEE, New York, pp 295–303 Google Scholar
  8. 8.
    Gössler G, Sifakis J (2005) Composition for component-based modeling. Sci Comput Program 55(1–3):161–183 zbMATHCrossRefGoogle Scholar
  9. 9.
    Gössler G, Xu DN, Girault A (2012) Probabilistic contracts for component-based design. Research report 7328, INRIA Google Scholar
  10. 10.
    Hermanns H (2002) Interactive Markov chains: the quest for quantified quality. LNCS, vol 2428. Springer, Berlin zbMATHCrossRefGoogle Scholar
  11. 11.
    Jonsson B, Larsen KG (1991) Specification and refinement of probabilistic processes. In: Symposium on logic in computer science, LICS’91. IEEE Computer Society, Los Alamitos, pp 266–277 Google Scholar
  12. 12.
    Katoen J-P, Klink D, Neuhäußer MR (2009) Compositional abstraction for stochastic systems. In: International conference on formal modeling and analysis of timed systems, FORMATS’09. LNCS, vol 5813. Springer, Berlin, pp 195–211 CrossRefGoogle Scholar
  13. 13.
    Kwiatkowska MZ, Norman G, Parker D, Qu H (2010) Assume-guarantee verification for probabilistic systems. In: International conference on tools and algorithms for the construction and analysis of systems, TACAS’10. LNCS, vol 6015. Springer, Berlin, pp 23–37 CrossRefGoogle Scholar
  14. 14.
    Meyer B (1991) Design by contract. In: Advances in object-oriented software engineering. Prentice Hall, New York, pp 1–50 Google Scholar
  15. 15.
    Morgan C, McIver A, Seidel K (1996) Probabilistic predicate transformers. ACM Trans Program Lang Syst 18(3):325–353 CrossRefGoogle Scholar
  16. 16.
    Raclet J-B, Badouel E, Benveniste A, Caillaud B, Passerone R (2009) Why modalities are good for interface theories? In: International conference on application of concurrency to system design, ACSD’09. IEEE, New York, pp 119–127 CrossRefGoogle Scholar
  17. 17.
    Xu DN, Gössler G, Girault A (2010) Probabilistic contracts for component-based design. In: International symposium on automated technology for verification and analysis, ATVA’10. LNCS, vol 6252. Springer, Berlin, pp 325–340 CrossRefGoogle Scholar
  18. 18.
    Yi W (1994) Algebraic reasoning for real-time probabilistic processes with uncertain information. In: Third international symposium on formal techniques in real-time and fault-tolerant systems, FTRTFT’94. LNCS, vol 863. Springer, Berlin, pp 680–693 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.INRIA Grenoble-Rhône-AlpesUniversity of GrenobleGrenobleFrance
  2. 2.INRIA Paris-RocquencourtParisFrance

Personalised recommendations