Underspecification, Inherent Nondeterminism and Probability in Sequence Diagrams

  • Atle Refsdal
  • Ragnhild Kobro Runde
  • Ketil Stølen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4037)


Nondeterminism in specifications may be used for at least two different purposes. One is to express underspecification, which means that the specifier for the same environment behavior allows several alternative behaviors of the specified component and leaves the choice between these to those responsible for implementing the specification. In this case a valid implementation will need to implement at least one, but not necessarily all, alternatives. The other purpose is to express inherent nondeterminism, which means that a valid implementation needs to reflect all alternatives. STAIRS is an approach to the compositional and incremental development of sequence diagrams supporting underspecification as well as inherent nondeterminism. Probabilistic STAIRS builds on STAIRS and allows probabilities to be included in the specifications. Underspecification with respect to probabilities is also allowed. This paper investigates the use of underspecification, inherent nondeterminism and probability in sequence diagrams, the relationships between these concepts, and how these are expressed in STAIRS and probabilistic STAIRS.


Composition Operator Semantic Representation Sequence Diagram Probabilistic Choice Nondeterministic Choice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [DH01]
    Damm, W., Harel, D.: LSCs: Breathing life into message sequence charts. Formal Methods in System Design 19(1), 45–80 (2001)CrossRefMATHGoogle Scholar
  2. [Dij76]
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)MATHGoogle Scholar
  3. [Heh04]
    Hehner, E.C.R.: Probabilistic predicative programming. In: Kozen, D., Shankland, C. (eds.) MPC 2004. LNCS, vol. 3125, pp. 169–185. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. [HHRS05a]
    Haugen, Ø., Husa, K.E., Runde, R.K., Stølen, K.: Why timed sequence diagrams require three-event semantics. Technical Report 309, Department of Informatics, University of Oslo (2005)Google Scholar
  5. [HHRS05b]
    Haugen, Ø., Husa, K.E., Runde, R.K., Stølen, K.: STAIRS towards formal design with sequence diagrams. Software and System Modeling 4(4), 349–458 (2005)CrossRefGoogle Scholar
  6. [HM03]
    Harel, D., Marelly, R.: Come, Let’s Play: Scenario-Based Programming Using LSC’s and the Play-Engine. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. [Hoa85]
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)MATHGoogle Scholar
  8. [ISO89]
    International Standards Organization. Information Processing Systems – Open Systems Interconnection - Lotos – a Formal Description Technique Based on the Temporal Ordering of Observational Behaviour – ISO 8807 (1989)Google Scholar
  9. [ITU99]
    International Telecommunication Union. Recommendation Z.120 — Message Sequence Chart (MSC) (1999)Google Scholar
  10. [MM99]
    Morgan, C., McIver, A.: pGCL: Formal reasoning for random algorithms. South African Computer Journal 22, 14–27 (1999)Google Scholar
  11. [OMG04]
    Object Management Group. UML 2.0 Superstructure Specification, ptc/04-10-02 edition (2004)Google Scholar
  12. [RHS05a]
    Refsdal, A., Husa, K.E., Stølen, K.: Specification and refinement of soft real-time requirements using sequence diagrams. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 32–48. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. [RHS05b]
    Refsdal, A., Husa, K.E., Stølen, K.: Specification and refinement of soft real-time requirements using sequence diagrams. Technical Report 323, Department of Informatics, University of Oslo (2005)Google Scholar
  14. [RHS05c]
    Runde, R.K., Haugen, Ø., Stølen, K.: Refining UML interactions with underspecification and nondeterminism. Nordic Journal of Computing 12(2), 157–188 (2005)MathSciNetMATHGoogle Scholar
  15. [Ros95]
    Roscoe, A.W.: CSP and determinism in security modelling. In: Proc. IEEE Symposium on Security and Privacy, pp. 114–127. IEEE Press, Los Alamitos (1995)Google Scholar
  16. [RRS06]
    Refsdal, A., Runde, R.K., Stølen, K.: Underspecification, inherent nondeterminism and probability in sequence diagrams. Technical Report 335, Department of Informatics, University of Oslo (2006)Google Scholar
  17. [SBDB97]
    Steen, M.W.A., Bowman, H., Derrick, J., Boiten, E.A.: Disjunction of LOTOS specifications. In: Mizuno, T., Shiratori, N., Higashino, T., Togashi, A. (eds.) Formal Description Techniques and Protocol Specification, Testing and Verification: FORTE X / PSTV XVII 1997, pp. 177–192. Chapman & Hall, Boca Raton (1997)CrossRefGoogle Scholar
  18. [Seg95]
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology (1995)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2006

Authors and Affiliations

  • Atle Refsdal
    • 1
    • 2
  • Ragnhild Kobro Runde
    • 1
  • Ketil Stølen
    • 1
    • 2
  1. 1.Department of InformaticsUniversity of OsloNorway
  2. 2.SINTEF ICTNorway

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