A compositional algebra, called mMCAN, for the execution time analysis of highlevel software processes is introduced. In mMCAN, processes can be concatenated, concurrently executed, and recursively invoked. We show that the set of execution times of an mMCAN is semilinear. We then propose and analyze an algorithm which calcuates the execution time sets of an mMCAN in semilinear forms. Finally, we consider several interesting variations of mMCAN whose execution time sets can be computed with algorithms.


real-time specification verification software recursion context-free semilinear 


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  1. 1.
    R. Alur, C. Courcoubetis, D.L. Dill. Model Checking for Real-Time Systems. 5th IEEE LICS, 1990.Google Scholar
  2. 2.
    R. Alur, T.A. Henzinger, P.-H. Ho. Automatic Symbolic Verification of Embedded Systems, in Proceedings of 1993 IEEE Real-Time System Symposium.Google Scholar
  3. 3.
    J.C.M. Baeten, J.A. Bergstra, J.W. Klop. Decidability of Bisimulation Equivalence for Process Generating Context-Free Languages. Tech. Rep. CS-R8632, 1987, CWI.Google Scholar
  4. 4.
    J.R. Burch, E.M. Clarke, K.L. McMillan, D.L.Dill, L.J. Hwang. Symbolic Model Checking: 1020 States and Beyond. 5th IEEE LICS, 1990.Google Scholar
  5. 5.
    A. Bouajjani, R. Echahed, P. Habermehl. On the Verification Problem of Nonregular Properties for Nonregular Processes. 10th IEEE LICS, 1995.Google Scholar
  6. 6.
    E. Clarke, E.A. Emerson, and A.P. Sistla. Automatic Verification of Finite-State Concurrent Systems Using Temporal Logic Specifications. ACM TOPLAS 8(2), 1986, pp. 244–263.CrossRefMATHGoogle Scholar
  7. 7.
    N. Chomsky. One Certain Formal Properties of Grammar. Information and Control, 2:2, 137–167.Google Scholar
  8. 8.
    S. Ginsburg, S.A. Greibach. Deterministic Context-Free Languages. Information and Control, 9:6, 563–582.Google Scholar
  9. 9.
    D. Harel. Statecharts: A Visual Formalism for Complex Systems.” The Weizmann Institute of Science Technical Report, Israel (July 1986). Also in Science of Programming 8, 1987.Google Scholar
  10. 10.
    T.A. Henzinger, Z. Manna, A. Pnueli. Temporal Proof Methodologies for Real-Time Systems. 18th ACM POPL, 1991.Google Scholar
  11. 11.
    T.A. Henzinger, X. Nicollin, J. Sifakis, S. Yovine, Symbolic Model Checking for Real-Time Systems, 7th IEEE LICS, 1992.Google Scholar
  12. 12.
    J.E. Hopcroft, J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.Google Scholar
  13. 13.
    F. Jahanian, A.K. Mok. Modechart: A Specification Language for Real-Time Systems.” to appear in IEEE Transactions on Software Engineering.Google Scholar
  14. 14.
    X. Nicollin, J. Sifakis, S. Yovine. From ATP to Timed Graphs and Hybrid Systems. In Real-Time: Theory in Practice, LNCS 600, Springer-Verlag, 1991.Google Scholar
  15. 15.
    R.J. Parikh. On Context-Free Languages. Journal of the Association for Computing Machinery, 4 (1966), 570–581.CrossRefMATHGoogle Scholar
  16. 16.
    F. Wang, A.K. Mok, E.A. Emerson. Real-Time Distributed System Specification and Verification in APTL. ACM TOSEM, Vol. 2, No. 4, Octobor 1993, pp. 346–378. Also in 14th ACM ICSE, 1992.CrossRefGoogle Scholar
  17. 17.
    F. Wang. Timing Behavior Analysis for Real-Time Systems. 10th IEEE LICS, San Diego, 1995.Google Scholar
  18. 18.
    F. Wang, C.T. Lo. Procedure-Level Verification of Real-Time Concurrent Systems. in Proceedings of the 3rd FME, Oxford, Britain, March 1996; LNCS 1051, Springer-Verlag.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Farn Wang
    • 1
  1. 1.Institute of Information ScienceAcademia SinicaTaipeiChina

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