Progressive Solutions to a Parallel Automata Equation

  • Sergey Buffalov
  • Khaled El-Fakih
  • Nina Yevtushenko
  • Gregor v. Bochmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2767)


In this paper, we consider the problem of deriving a component X of a system knowing the behavior of the whole system C and the other components A. The component X is derived by solving the parallel automata equation \(A \Diamond X \cong C\). We present algorithms for deriving the largest progressive solution to the equation that combined with A does not block any possible action in C and we introduce a new simulation relation between automata in order to characterize all progressive solutions.


  1. 1.
    Barrett, G., Lafortune, S.: Bisimulation: The Supervisory Control Problem, and Strong Model Matching for Finite State Machines. Discrete Event Dynamic Systems: Theory and Application 8(4), 377–429 (1998)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bochmann G.v., Merlin, P.: On the Construction of Communication Protocols. In: ICCC, pp. 371–378 (1980); reprinted in: Sunshine, C. (ed.): Communication Protocol Modeling. Artech House Publ. (1981)Google Scholar
  3. 3.
    Drissi, J., Bochmann, G.v.: Submodule Construction for Systems of I/O Automata,
  4. 4.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  5. 5.
    Kelekar, S.G.H.: Synthesis of Protocols and Protocol Converters Using the Submodule Construction Approach. In: Danthine, A., et al. (eds.) Proc. PSTV, XIII (1994)Google Scholar
  6. 6.
    Kumar, R., Nelvagal, S., Marcus, S.I.: A Discrete Event Systems Approach for Protocol Conversion. Discrete Event Dynamical Systems: Theory and Applications 7(3), 295–315 (1997)CrossRefMATHGoogle Scholar
  7. 7.
    Merlin, P., Bochmann, G.v.: On the Construction of Submodule Specifications and Communication Protocols. ACM Trans. On Programming Languages and Systems 5(1), 1–25 (1983)CrossRefMATHGoogle Scholar
  8. 8.
    Parrow, J.: Submodule Construction as Equation Solving in CCS. Theoretical Computer Science 68 (1989)Google Scholar
  9. 9.
    Petrenko, A., Yevtushenko, N.: Solving Asynchronous Equations. In: Proc. of IFIP FORTE/PSTV 1998 Conf., Chapman-Hall, Boca Raton (1998)Google Scholar
  10. 10.
    Petrenko, A., Yevtushenko, N., Bochmann, G.v., Dssouli, R.: Testing in Context: Framework and Test Derivation. Computer Communications Journal, Special issue on Protocol engineering 19, 1236–1249 (1996)Google Scholar
  11. 11.
    Qin, H., Lewis, P.: Factorisation of Finite State machines Under Strong and Observational Equivalences. Journal of Formal Aspects of Computing 3, 284–307 (1991)CrossRefMATHGoogle Scholar
  12. 12.
    Tao, Z., Bochmann, G.v., Dssouli, R.: A Formal Method for Synthesizing Optimized Protocol Converters and its Application to Mobile Data Networks. Mobile Networks & Applications 2(3), 259–269 (1997)CrossRefGoogle Scholar
  13. 13.
    Wonham, W.M., Ramadge, P.J.: On the Supremal Controllable Sublanguage of a Given Language. SIAM J. Control. Optim. 25(3), 637–659 (1987)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yevtushenko, N., Villa, T., Brayton, R.K., Petrenko, A., Sangiovanni-Vincentelli, A.: Solving a Parallel Language Equation. In: Proc. of the ICCAD 2001, USA (2001)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2003

Authors and Affiliations

  • Sergey Buffalov
    • 1
  • Khaled El-Fakih
    • 2
  • Nina Yevtushenko
    • 1
  • Gregor v. Bochmann
    • 3
  1. 1.Tomsk State UniversityRussia
  2. 2.Department of Computer ScienceAmerican University of SharjahUAE
  3. 3.School of Information Technology and EngineeringUniversity of OttawaCanada

Personalised recommendations