Liveness, Fairness and Impossible Futures

  • Rob van Glabbeek
  • Marc Voorhoeve
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)

Abstract

Impossible futures equivalence is the semantic equivalence on labelled transition systems that identifies systems iff they have the same “AGEF” properties: temporal logic properties saying that reaching a desired outcome is not doomed to fail. We show that this equivalence, with an added root condition, is the coarsest congruence containing weak bisimilarity with explicit divergence that respects deadlock/livelock traces (or fair testing, or any liveness property under a global fairness assumption) and assigns unique solutions to recursive equations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aceto, L.(moderator): Some open problems in Process Algebra (2003), http://www.cs.auc.dk/luca/BICI/open-problems.html
  2. 2.
    Baeten, J.C.M. (ed.): Applications of Process Algebra. Cambridge Tracts in Theoretical Computer Science 17. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  3. 3.
    Baeten, J.C.M., Bergstra, J.A., Klop, J.W.: On the consistency of Koomen’s fair abstraction rule. Theoretical Computer Science 51(l/2), 129–176 (1987)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Bloom, B., Istrael, S., Meyer, A.: Bisimulation Can’t Be Traced. Journal of the ACM 42(1), 232–268 (1995)CrossRefMATHGoogle Scholar
  5. 5.
    Brinksma, E., Rensink, A., Vogler, W.: Fair Testing. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 311–327. Springer, Heidelberg (1995); Journal preprint: http://eprints.eemcs.utwente.nl/1623/01/submitted.pdf
  6. 6.
    Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. Journal of the ACM 31(3), 560–599 (1984)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  8. 8.
    De Nicola, R., Vaandrager, F.W.: Three logics for branching bisimulation. Journal of the ACM 42(2), 458–487 (1995)CrossRefMATHGoogle Scholar
  9. 9.
    Francez, N.: Fairness. Springer, Heidelberg (1986)MATHGoogle Scholar
  10. 10.
    van Glabbeek, R.J.: The Linear Time – Branching Time Spectrum II: The semantics of sequential systems with silent moves (extended abstract). In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)Google Scholar
  11. 11.
    van Glabbeek, R.J.: A Characterisation of Weak Bisimulation Congruence. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity: Essays Dedicated to J.W. Klop, On the Occasion of His 60th Birthday, LNCS, vol. 3838, pp. 26–39. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Milner, R.: Communication and Concurrency. Prentice-Hall International, Englewood Cliffs (1990); In: Milner, R.(ed.) A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980) (earlier version appeared) Google Scholar
  13. 13.
    Vogler, W.: Modular Construction and Partial Order Semantics of Petri Nets. LNCS, vol. 625. Springer, Heidelberg (1992)Google Scholar
  14. 14.
    Voorhoeve, M., Mauw, S.: Impossible Futures and Determinism. Information Processing Letters 80(1), 51–58 (2001)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rob van Glabbeek
    • 1
    • 2
  • Marc Voorhoeve
    • 3
  1. 1.National ICT AustraliaSydney
  2. 2.School of Computer Science and EngineeringThe University of New South Wales 
  3. 3.Dept. of Mathematics and Computer ScienceEindhoven University of Technology 

Personalised recommendations