Coalgebraic Semantic Model for the Clock Constraint Specification Language

  • Frédéric MalletEmail author
  • Grygoriy Zholtkevych
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 476)


The Clock Constraint Specification Language (ccsl) has initially been introduced as part of the uml Profile for marte dedicated to the modeling and analysis of real-time and embedded systems. ccsl proposes a set of simple patterns classically used to specify causal and temporal properties of (uml/EMF) models. The paper proposes a new semantic model for ccsl based on the notion of “clock coalgebra”. Co-algebra promises to give a unified framework to study the behavior and semantics of reactive systems and, more generally, infinite data structures. They appear as being the adequate mathematical structure to capture the infinite nature of ccsl operators. This paper proposes a co-algebraic structure for ccsl, or rather a natural generalization of ccsl that we call generalized clock constraints: GenCCSL. We establish that GenCCSL covers the class of ccsl constraints and we give examples of GenCCSL constraints that cannot be expressed with classical ccsl. Then, we discuss the properties of the newly introduced class, including ways to detect valid and invalid GenCCSL behaviors, as well as deciding whether a GenCCSL constraint is also a ccsl one.


Concurrent system Behavior model Clock model Transition system Coalgebra 


  1. 1.
    André, C.: Syntax and semantics of the Clock Constraint Specification Language (CCSL). Research report 6925, INRIA, May 2009.
  2. 2.
    André, C., Mallet, F., DeAntoni, J.: VHDL observers for clock constraint checking. In: International Symposium on Industrial Embedded Systems (SIES), pp. 98–107. IEEE, Trento, Italy, July 2010.
  3. 3.
    André, C., Mallet, F., de Simone, R.: Modeling time(s). In: Engels, G., Opdyke, B., Schmidt, D.C., Weil, F. (eds.) MODELS 2007. LNCS, vol. 4735, pp. 559–573. Springer, Heidelberg (2007). 38 CrossRefGoogle Scholar
  4. 4.
    Benveniste, A., Caspi, P., Edwards, S.A., Halbwachs, N., Le Guernic, P., de Simone, R.: The synchronous languages 12 years later. Proc. IEEE 91(1), 64–83 (2003)CrossRefGoogle Scholar
  5. 5.
    Dang, Z.: Binary reachability analysis of pushdown timed automata with dense clocks. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 506–518. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  6. 6.
    DeAntoni, J., Mallet, F.: TimeSquare: treat your models with logical time. In: Furia, C.A., Nanz, S. (eds.) TOOLS 2012. LNCS, vol. 7304, pp. 34–41. Springer, Heidelberg (2012). 4 CrossRefGoogle Scholar
  7. 7.
    Gupta, G., Saeedloei, N., DeVries, B., Min, R., Marple, K., Kluźniak, F.: Infinite computation, co-induction and computational logic. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 40–54. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  8. 8.
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)CrossRefzbMATHGoogle Scholar
  9. 9.
    Mallet, F.: Logical Time @ Work for the Modeling and Analysis of Embedded Systems. LAMBERT Academic Publishing, January 2011, ISBN: 978-3-8433-9388-1Google Scholar
  10. 10.
    Mallet, F., André, C.: On the semantics of UML/Marte clock constraints. In: 2009 IEEE International Symposium on Object/Component/Service-Oriented Real-Time Distributed Computing, ISORC, pp. 305–312. IEEE Computer Press, Tokyo, March 2009.
  11. 11.
    Mallet, F., Millo, J.V., de Simone, R.: Safe CCSL specifications and marked graphs. In: 11th ACM/IEEE International Conference on Formal Methods and Models for Codesign, MEMOCODE, pp. 157–166. IEEE (2013).
  12. 12.
    Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70. Springer, Heidelberg (1979). CrossRefGoogle Scholar
  13. 13.
    OMG: UML Profile for MARTE, v1.0. Object Management Group, November 2009, formal/2009-11-02Google Scholar
  14. 14.
    Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algebr. Program. 60–61, 17–139 (2004)MathSciNetGoogle Scholar
  15. 15.
    Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000). CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5(2), 285–309 (1955). CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Zholtkevych, G., Mallet, F., Zaretska, I., Zholtkevych, G.: Two semantic models for clock relations in the clock constraint specification language. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2013. CCIS, vol. 412, pp. 190–209. Springer, Heidelberg (2013). 10 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University Nice Sophia Antipolis, CNRS, I3S, UMR 7271Sophia AntipolisFrance
  2. 2.INRIA Sophia Antipolis MéditerranéeSophia AntipolisFrance
  3. 3.East China Normal University/Software Engineering InstituteShanghaiPeople’s Republic of China
  4. 4.Deparment of Theory and Application in ComputerscienceV.N. Karazin Kharkiv National UniversityKharkivUkraine

Personalised recommendations