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Completeness and Decidability of a Fragment of Duration Calculus with Iteration

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Book cover Advances in Computing Science — ASIAN’99 (ASIAN 1999)

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Abstract

Duration Calculus with Iteration (DC*) has been used as an interface between original Duration Calculus and Timed Automata, but has not been studied rigorously. In this paper, we study a subset of DC* formulas consisting of so-called simple ones which corresponds precisely with the class of Timed Automata. We give a complete proof system and the decidability results for the subset.

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References

  1. Abramsky, S., Gabbay, D., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science. Clarendon Press, Oxford (1992).

    Google Scholar 

  2. Alur, R., Dill, D.L.: A Theory of Timed Automata. Theoretical Computer Science.126 (1994) 183–235.

    Article  MATH  MathSciNet  Google Scholar 

  3. Asarin, E., Caspi, P., Maler, O.: A Kleene Theorem for Timed Automata. In: Winskel, G. (Ed.): Proceedings of IEEE International Symposium on Logics in Com-puter Science LICS’97. IEEE Computer Society Press (1997) 160–171.

    Google Scholar 

  4. . Dang Van, H., Wang Ji: On The Design of Hybrid Control Systems Using Automata Models. In Chandru, V, Vinay, V. (eds.): Theoretical Computer Science. LNCS 1180. Springer-Verlag (1996) 415–438.

    Google Scholar 

  5. Dang Van, H., Pham, H.T.: On Checking Parallel Real-Time Systems for Linear Duration Invariants. In Kramer, B., Uchihita, N., Croll, P., Russo, S. (eds.): Pro-ceedings of PDSE’98. IEEE Computer Society Press (1998) 61–71.

    Google Scholar 

  6. Dang Van, H., Guelev, Dimitar P.: Completeness and Decidability of a Fragment of Duration Calculus with Iterations. Technical Report 163, UNU/IIST, P.O.Box3058, Macau, 1998.

    Google Scholar 

  7. Dutertre, B.: On First Order Interval Temporal Logic Report No. CSD-TR-94-3. Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, England, 1995.

    Google Scholar 

  8. Guelev, D.P.: A Calculus of Durations on Abstract Domains: Completeness and Extensions. Technical Report 139, UNU/IIST, P.O.Box 3058, Macau, 1998.

    Google Scholar 

  9. Hansen, M.R., Zhou, C.C.: Semantics and Completeness of Duration Calculus. In: Real-Time: Theory and Practice. LNCS 600. Springer-Verlag (1992) 209–225.

    Google Scholar 

  10. Hansen, M.R., Zhou, C.C.: Duration Calculus: Logical Foundations. Formal As-pects of Computing 9 (1997) 283–330.

    Article  MATH  Google Scholar 

  11. Li, X.D., Dang Van, H.: Checking Linear Duration invariants by Linear Program-ming. In: Ja_ar, J., Yap, R.H.C. (eds.): Concurrency and Paralellism, Programming, Networking, and Security. LNCS 1179. Springer-Verlag (1996) 321–332.

    Google Scholar 

  12. Pandya, P.K.: Some Extensions to Mean-Value Calculus: Expressiveness and De-cidability. In: Buning, H.K.(ed), Proc. CSL’95. LNCS 1092. Springer-Verlag (1995).

    Google Scholar 

  13. Shoenfield, J.: Mathematical Logic. Addison-Wesley, Massachusetts (1967).

    MATH  Google Scholar 

  14. Zhou, C.C., Hoare, C. A. R., Ravn, A. P.: A Calculus of Durations. Information Processing Letters, 40(5) (1991) 269–276.

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhou, C.C., Zhang, J.Z., Yang, L., and Li, X.S.: Linear Duration Invariants. In: Formal Techniques in Real-Time and Fault-Tolerant systems. LNCS 863. (1994).

    Google Scholar 

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Authors and Affiliations

  1. International Institute for Software Technology, The United Nations University, P.O.Box 3058, Macau

    Dang Van Hung & Dimitar P. Guelev

Authors
  1. Dang Van Hung
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  2. Dimitar P. Guelev
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Editors and Affiliations

  1. Chennai Mathematical Institute, 92 G.N. Chetty Road, T. Nagar, Chennai, 600 017, India

    P. S. Thiagarajan

  2. School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    Roland Yap

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© 1999 Springer-Verlag Berlin Heidelberg

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Van Hung, D., Guelev, D.P. (1999). Completeness and Decidability of a Fragment of Duration Calculus with Iteration. In: Thiagarajan, P.S., Yap, R. (eds) Advances in Computing Science — ASIAN’99. ASIAN 1999. Lecture Notes in Computer Science, vol 1742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46674-6_13

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  • DOI: https://doi.org/10.1007/3-540-46674-6_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66856-5

  • Online ISBN: 978-3-540-46674-1

  • eBook Packages: Springer Book Archive

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