Skip to main content
Log in

TIC: A timed calculus

  • Published:
Formal Aspects of Computing

Abstract

TIC is a timed algebraic calculus which combines ideas from asynchronous and synchronous calculi. Time is introduced by assigning explicit time restrictions to the events of an asynchronous calculus. The semantics is defined in an operational way. Interleaving of behaviours is defined in such a way that a proper merge of events in time is achieved. Weak timed bisimulation is also defined. Examples are presented to show the applicability of the calculus to the study of timed behaviours.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Austry, D. and Boudol, G.: Algebre de Processus et Synchronisation.J TCS, 53:225–241, 1987.

    Google Scholar 

  2. Azcorra, A.:Modelado Formal de Sistemas Sincronos. PhD thesis, Escuela Tecnica Superior de Ingenieros de Telecomunicacion, Universidad Politecnica de Madrid, 1989.

  3. Baeten, J. C. M. and Bergstra, J. A.: Real Time Process Algebra.Formal Aspects of Computing, 3(2):142–188, 1991.

    Google Scholar 

  4. Bergstra, J. A. and Klop, J. W.: Algebra of Communicating Processes with Abstraction.Theoretical Computer Science, 37(1):77–121, 1985.

    Google Scholar 

  5. Bolognesi, T. and Lucidi, F.: LOTOS-like Process Algebras with Urgent or Timed Interactions. InFORTE'91: Formal Techniques IV, Sidney, November 1991.

  6. Bolognesi, T., Lucidi, F. and Trigila, S.: From Timed Petri Nets to Timed LOTOS. In L. Logrippo, R. Probert, and H. Ural, editors,Tenth International IFIP Symposium on Protocol Specification, Testing and Verification, pages 377–406. North-Holland, June 1990.

  7. Bolognesi, T. and Rudin, H.: On the Analisys of Time-Dependent Protocols by Network Flow Algorithms. InFifth International Workshop on Protocol Specification, Testing and Verification, New York, June 1985.

  8. Brinksma, E., Scollo, G. and Steenbergen, C.: LOTOS Specifications, their Implementation and their Tests. InSixth International Workshop on Protocol Specification, Testing and Verification, Montreal, June 1986.

  9. Nicola, R. de. and Hennessy, M.: Testing Equivalences for Processes.Theoretical Computer Science, 34(1,2):83–133, Nov 1984.

    Google Scholar 

  10. Gerth, R. and Boucher, A.:A timed Failures Model for Extended Communicating Processes, volume LNCS. ICALP 87, 1987.

  11. Hoare, C.A.R.:Communicating Sequential Processes. Prentice-Hall Int., 1985.

  12. Hennessy, M. and Regan, T.: A Temporal Process Algebra. InFORTE'90: Formal Techniques III, Madrid, November 1990.

  13. ISO. LOTOS a Formal Description Technique based on the Temporal Ordering of Observational Behaviour. IS 8807, TC97/SC21, 1988.

  14. Koymans, R., et al.: Compositional Semantics for Real Time Distributed Computing. InConference on Logics of Programs. Springer Verlag, 1985.

  15. Leveson, N.G. and Stolzy, J.L.: Safety analysis using Petri nets.IEEE Transactions on Software Engineering, 13(3), 1987.

  16. Merlin, P. M. and Farber, D. J.: Recoverability of Communication Protocols — Implication of a theoretical Study.IEEE Trans, on Com., 24:1036–1043, Sep 1976.

    Google Scholar 

  17. Nieto, C. M.:Tecnicas de descripcion Formal aplicadas la Evaluacion de Prestaciones de Sistemas de Comunicacion. PhD thesis, Escuela Tecnica Superior de Ingenieros de Telecomunicacion, Universidad Politecnica de Madrid, 1991.

  18. Milner, R.:Calculus of Communicating Systems. Number 92 in Lecture Notes in Computer Science. Springer Verlag, Berlin, 1980.

    Google Scholar 

  19. Milner, R.: Calculi for Synchrony and Asynchrony.Theoretical Computer Science, 25:267–310, 1983.

    Google Scholar 

  20. Milne, G.: CIRCAL and the Representation of Communication, Concurrency and Time.ACM, TOPLAS, 7(2):270–298, April 1985.

    Google Scholar 

  21. Moller, F. and Tofts, C.:A Temporal Calculus of Communicating Systems, pages 401–415. Number LNCS-458, ISBN 3-540-53048-7 in Lecture Notes in Computer Science. Springer-Verlag, Berlin Heidelberg, New York, 1990.

    Google Scholar 

  22. Nicollin, X., Ritchier, J. L., Sifakis, J. and Voiron, J.: ATP: An Algebra for Timed Processes. InTC2 Working Conference on Programming Concepts and Methods. North Holland, 1990.

  23. Ortega, Y. and de Frutos, D.: Timed Observations: A semantic Model for Real-Time Concurrency. InTC2 Working Conference on Programming Concepts and Methods. North Holland, 1990.

  24. Ortega, Y. and de Frutos, D.: A Complete Proof System for Timed Observations. InTAPSOFT'91 (CAAP'91). LNCS 493, Springer Verlag, 1991.

  25. Park, D.:Concurrency and Automata on Infinite Sequences, volume 104 ofLNCS. Springer-Verlag, 1981.

  26. Quemada, J., Azcorra, A. and de Frutos, D.: A Timed Calculus for LOTOS. InFORTE'89: Formal Techniques II, Vancouver, December 1989.

  27. Quemada, J. and Fernandez, A.: Introduction of Quantitative Relative Time into LOTOS. InIFIP workshop on Protocol Specification, Testing and Verification: VII, Zurich, May 5, 1987.

  28. Quemada, J., Pavon, S. and Fernandez, A.: State Exploration by Transformation with LOLA. InWorkshop on Automatic Verification Methods for Finite State Systems, Grenoble, June 1989.

  29. Reed, G. M. and Roscoe, A. W.: A timed model for communicating sequential processes. InICALP 86, volume LNCS 226. Springer Verlag, 1986.

  30. Reed, G. M. and Roscoe, A. W.:Metric Spaces as Models for Real-Time Concurrency. Springer Verlag, 1987.

  31. Tofts, C.: Temporal Ordering for Concurrency. Technical report, University of Edinburgh, April 1988.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Juan Quemada.

Additional information

This work was partially supported by CICYT under the TIC program (MEDAS project)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Quemada, J., de Frutos, D. & Azcorra, A. TIC: A timed calculus. Formal Aspects of Computing 5, 224–252 (1993). https://doi.org/10.1007/BF01211556

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01211556

Keywords

Navigation