Property preserving simulations

  • S. Bensalem
  • A. Bouajjani
  • C. Loiseaux
  • J. Sifakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 663)


We study property preserving transformations for reactive systems. A key idea is the use of <ϕ, ψ>-simulations which are simulations parameterized by a Galois connection (ϕ, ψ), relating the lattices of properties of two systems.

We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function ϕ mapping sets of states of a system S into sets of states of a system S'. Roughly speaking, ϕ preserves f if the satisfaction of f at some state of S implies that f is satisfied by any state in the image of this state by ϕ.

The main results concern the preservation of properties expressed in sublanguages of the branching time μ-calculus when two systems S and S' are related via <ϕ,ψ>-simulations. They can be used in particular to verify a property for a system by proving this property on a simpler system which is an abstraction of it.


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  1. [AL88]
    M. Abadi and L. Lamport. The existence of Refinement Mappings. SRC 29, Digital Equipment Corpoiation, Systems Research Center, August 1988.Google Scholar
  2. [BFG*91]
    A. Bouajjani, J.C. Fernandez, S. Graf, C. Rodriguez, and J. Sifakis. Safety for branching time semantics. In J.L. Albert, B. Monein, and M.R. Artalejo, editors, 18th ICALP, pages 76–92, LNCS 510, Springer-Verlag, October 1991.Google Scholar
  3. [Bou89]
    A. Bouajjani. From Linear-Time Propositional Temporal Logics to a Branching-Time μ-calculus. RTC 15, LGI-IMAG, Grenoble, 1989.Google Scholar
  4. [Bra78]
    D. Brand. Algebraic simulation between parallel programs. RC 7206 30923, IBM, Yorktown Heights, 1978.Google Scholar
  5. [Buc62]
    J.R. Büchi. On a decision method in restricted second order arithmetic. In Intern. Cong. Logic, Method and Philos. Sci., Stantford Univ. Press, 1962.Google Scholar
  6. [CC79]
    P. Cousot and R. Cousot. Systematic design of program analysis framework. In Proc. 6th ACM Symp. on Principle of Programming Languages, 1979.Google Scholar
  7. [CC90]
    P. Cousot and R. Cousot. Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation. Technical Report, LIX, Ecole Polytechnique, May 1990.Google Scholar
  8. [CES83]
    E. M. Clarke, E. A. Emerson, and E. Sistla. Automatic Verification of Finite State Concurrent Systems using Temporal Logic Specifications: A Practical Approach. In 10th Symposium on Principles of Programming Languages (POPL 83), ACM, 1983. Complete version published in ACM TOPLAS, 8(2):244–263, April 1986.Google Scholar
  9. [CGL92]
    E.M. Clarke, O. Grumberg, and D.E. Long. Model checking and abstraction. In Symposium on Principles of Programming Languages (POPL 92), ACM, October 1992.Google Scholar
  10. [EH83]
    E.A. Emerson and J. Y. Halpern, 'sometimes’ and’ not never’ revisited: on branching versus linear time logic. In 10th. Annual Symp. on Principles of Programming Languages, 1983.Google Scholar
  11. [GS86a]
    S. Graf and J. Sifakis. A logic for the specification and proof of regular controllable processes of CCS. Acta Informatica, 23, 1986.Google Scholar
  12. [GS86b]
    S. Graf and J. Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68, 1986.Google Scholar
  13. [HM85]
    M. Hennessy and R. Milner. Algebraic laws for nondeterminism and concurrency. Journal of the Association for Computing Machinery, 32:137–161, 1985.Google Scholar
  14. [KM79]
    T. Kasai and R.E. Miller. Homomorphisms between models of parallel computation. RC 7796 33742, IBM, Yorktown Heights, 1979.Google Scholar
  15. [Koz83]
    D. Kozen. Results on the propositional μ-calculus. In Theoretical Computer Science, North-Holland, 1983.Google Scholar
  16. [Kur89]
    R.P. Kurshan. Analysis of Discrete Event Coordination. LNCS 430, Springer-Verlag, May 1989.Google Scholar
  17. [Lam77]
    L. Lamport. Proving the correctness of multiprocess programs. IEEE Transactions on Software Engineering, SE-3(2):125–143, 1977.Google Scholar
  18. [LPZ85]
    O. Lichtenstein, A. Pnueli, and L. Zuck. The glory of the past. In Conference on Logics of Programs, LNCS 194, Springer Verlag, 1985.Google Scholar
  19. [LT88]
    N.A. Lynch and M.R. Tuttle. An introduction to Input/Ouput Automata. MIT/LCS/TM 373, MIT, Cambridge, Massachussetts, November 1988.Google Scholar
  20. [Mil71]
    R. Milner. An algebraic definition of simulation between programs. In Proc. Second Int. Joint Conf. on Artificial Intelligence, pages 481–489, BCS, 1971.Google Scholar
  21. [MP90]
    Z. Manna and A. Pnueli. A hierarchy of temporal properties. In Proc. 9th ACM Symp. on Princ. of Dist. Comp., 1990.Google Scholar
  22. [NV90]
    R. De Nicola and F. Vaandrager. Three logics for branching bisimulation. In Proc. of Fifth Symp. on Logic in Computer Science, Computer Society Press, 1990.Google Scholar
  23. [Ore44]
    O. Ore. Galois connexions. Trans. Amer. Math. Soc, 55:493–513, February 1944.Google Scholar
  24. [Pnu77]
    A. Pnueli. The Temporal Logic of Programs. In 18th Symposium on Foundations of Computer Science (FOCS 77), IEEE, 1977. Revised version published in Theoretical Computer Science, 13:45–60, 1981.Google Scholar
  25. [San77]
    Luis E. Sanchis. Data types as lattices: retractions, projection and projection. In RAIRO Theorical computer science, vol 11, nomber 4, pages 339–344, 1977.Google Scholar
  26. [Sif82a]
    J. Sifakis. Property preserving homomorphisms and a notion of simulation of transition systems. RR IMAG 332, IMAG, November 1982.Google Scholar
  27. [Sif82b]
    J. Sifakis. A unified approach for studying the properties of transition systems. Theorical Computer Science, 18, 1982.Google Scholar
  28. [Sif83]
    J. Sifakis. Property preserving homomorphisms of transition systems. In E. Clarke and D. Kozen, editors, Workshop on logics of programs, LNCS 164, Springer-Verlag, 1983.Google Scholar
  29. [Wol83]
    P. Wolper. Temporal logic can be more expreessive. Inform. Contr., 56, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • S. Bensalem
    • 1
  • A. Bouajjani
    • 1
  • C. Loiseaux
    • 1
  • J. Sifakis
    • 1
  1. 1.IMAG-LGIGrenoble

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