Equivalences and preorders of transition systems

  • A. Arnold
  • A. Dicky
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)


Two transition systems are logically equivalent if they satisfy the same formulas of a given logic. For some of these logics, such as Hennessy-Milner's logic, there is an algebraic characterization of this equivalence involving particular homomorphisms of transition systems. This logical equivalence is associated with a preorder: a transition system S is less than S' if all formulas satisfied by S are satisfied by S'. For particular logics, this preorder can also be algebraically characterized, using homomorphisms and a specific notion of inclusion of transition systems.


bisimulation temporal logic transition system 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A92]
    A. Arnold. Systèmes de transitions finis et sémantique des processus communicants. Masson, 1992.Google Scholar
  2. [AD89]
    A. Arnold, A. Dicky. An Algebraic Characterization of Transition System Equivalences. Information and Computation, 82:198–229, 1989.Google Scholar
  3. [BL92]
    G. Boudol, K. Larsen. Graphical versus Logical Specifications. Theor. Comput. Sci.,106:3–20, 1992Google Scholar
  4. [DDN88]
    P. Degano, R. De Nicola, U. Montanari. A Distributed Operational Semantics for CCS Based on Condition/Event Systems, Acta Informatica, 26:59–91, 1988.Google Scholar
  5. [DV90]
    R. De Nicola, F. Vaandrager. Three Logics for Branching Bisimulation. in: Proc. of LICS '90(1990)118–129.Google Scholar
  6. [CES86]
    E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finite state concurrent systems using temporal logics specifications. ACM Trans. Prog. Lang. Syst., 8:244–263, 1986.Google Scholar
  7. [EH86]
    E. A. Emerson and J. Y. Halpern. “Sometimes” and “Not Never” revisited: on branching versus linear time temporal logic. J. Assoc. Comput. Mach., 33:151–178, 1986.Google Scholar
  8. [ES84]
    E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61:175–201, 1984.Google Scholar
  9. [HM85]
    M. Hennessy, R.Milner. Algebraic laws for nondeterminism and concurrency. J. Assoc. Comput. Mach., 32:137–161, 1985.Google Scholar
  10. [HS84]
    M. Hennessy, C. Stirling. The power of the future perfect in program logics. in: 11th Math. Foundations of Comput. Sci, 1984. Lect. Notes Comput. Sci. 176(1984)301–311.Google Scholar
  11. [LT88]
    K. Larsen, B. Thomsen. A Modal Process Logic. in: Proc. of LICS '88(1988)203–210.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • A. Arnold
    • 1
  • A. Dicky
    • 1
    • 2
  1. 1.LaBRI Université Bordeaux IFrance
  2. 2.IUT La RochelleFrance

Personalised recommendations