Revisiting Timed Specification Theories: A Linear-Time Perspective

  • Chris Chilton
  • Marta Kwiatkowska
  • Xu Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7595)


We consider the setting of component-based design for real-time systems with critical timing constraints. Based on our earlier work, we propose a compositional specification theory for timed automata with I/O distinction, which supports substitutive refinement. Our theory provides the operations of parallel composition for composing components at run-time, logical conjunction/disjunction for independent development, and quotient for incremental synthesis. The key novelty of our timed theory lies in a weakest congruence preserving safety as well as bounded liveness properties. We show that the congruence can be characterised by two linear-time semantics, timed-traces and timed-strategies, the latter of which is derived from a game-based interpretation of timed interaction.


Transition System Parallel Composition Game State Realisable Trace Asynchronous Circuit 
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  1. 1.
    Chen, T., Chilton, C., Jonsson, B., Kwiatkowska, M.: A Compositional Specification Theory for Component Behaviours. In: Seidl, H. (ed.) ESOP 2012. LNCS, vol. 7211, pp. 148–168. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    de Alfaro, L., Henzinger, T.A., Stoelinga, M.: Timed Interfaces. In: Sangiovanni-Vincentelli, A.L., Sifakis, J. (eds.) EMSOFT 2002. LNCS, vol. 2491, pp. 108–122. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata: a complete specification theory for real-time systems. In: HSCC 2010, pp. 91–100. ACM (2010)Google Scholar
  4. 4.
    de Alfaro, L., Henzinger, T.A.: Interface automata. SIGSOFT Softw. Eng. Notes 26, 109–120 (2001)CrossRefGoogle Scholar
  5. 5.
    Kaynar, D.K., Lynch, N.A., Segala, R., Vaandrager, F.W.: Timed I/O Automata: A mathematical framework for modeling and analyzing real-time systems. In: RTSS (2003)Google Scholar
  6. 6.
    Lim, W.: Design methodology for stoppable clock systems. Computers and Digital Techniques, IEE Proceedings E 133, 65–72 (1986)CrossRefGoogle Scholar
  7. 7.
    Moore, S.W., Taylor, G.S., Cunningham, P.A., Mullins, R.D., Robinson, P.: Using stoppable clocks to safely interface asynchronous and synchronous subsystems. In: AINT (Asynchronous INTerfaces) Workshop, Delft, Netherlands (2000)Google Scholar
  8. 8.
    Wang, X., Kwiatkowska, M.Z.: On process-algebraic verification of asynchronous circuits. Fundam. Inform. 80, 283–310 (2007)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Dill, D.L.: Trace theory for automatic hierarchical verification of speed-independent circuits. ACM distinguished dissertations. MIT Press (1989)Google Scholar
  10. 10.
    David, A., Larsen, K.G., Legay, A., Nyman, U., Wąsowski, A.: ECDAR: An Environment for Compositional Design and Analysis of Real Time Systems. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 365–370. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Bertrand, N., Legay, A., Pinchinat, S., Raclet, J.-B.: A Compositional Approach on Modal Specifications for Timed Systems. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 679–697. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Cerans, K., Godskesen, J.C., Larsen, K.G.: Timed Modal Specification - Theory and Tools. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 253–267. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  13. 13.
    Berendsen, J., Vaandrager, F.W.: Compositional Abstraction in Real-Time Model Checking. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 233–249. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Verhoeff, T.: A Theory of Delay-Insensitive Systems. PhD thesis, Dept. of Math. and C.S., Eindhoven Univ. of Technology (1994)Google Scholar
  15. 15.
    Zhou, B., Yoneda, T., Myers, C.: Framework of timed trace theoretic verification revisited. IEICE Trans. on Information and Systems 85, 1595–1604 (2002)Google Scholar
  16. 16.
    Chilton, C., Kwiatkowska, M., Wang, X.: Revisiting timed specification theories: A linear-time perspective. Technical Report RR-12-04, Department of Computer Science, University of Oxford (2012)Google Scholar
  17. 17.
    Wang, X.: Maximal Confluent Processes. In: Haddad, S., Pomello, L. (eds.) PETRI NETS 2012. LNCS, vol. 7347, pp. 188–207. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Thiele, L., Wandeler, E., Stoimenov, N.: Real-time interfaces for composing real-time systems. In: EMSOFT (2006)Google Scholar
  19. 19.
    Lee, I., Leung, J., Song, S.: Handbook of Real-Time and Embedded Systems. Chapman (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chris Chilton
    • 1
  • Marta Kwiatkowska
    • 1
  • Xu Wang
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK

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