From Transitions to Executions

  • Eleftherios Matsikoudis
  • Edward A. Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7399)


Interleaving theories have traditionally failed to integrate a satisfactory treatment of the so-called “finite delay property”. This is generally attributed to the expansion law of such theories, but in truth, the problem is rooted in the concept of labelled transition system. We introduce a new type of system, in which, instead of labelled transitions, we have, essentially, sequences of labelled transitions. We call systems of this type labelled execution systems. We use a coalgebraic representation to obtain, in a canonical way, a suitable concept of bisimilarity among such systems, study the conditions under which that concept agrees with the intuitive understanding of equivalence of branching structure that one has for these systems, and examine their relationship with labelled transition systems, precisely characterizing the difference in expressive power and branching complexity between the two kinds of systems.


Transition System Binary Relation Class Function Temporal Logic Label Transition System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abrahamson, K.: Decidability and Expressiveness of Logics of Programs. PhD thesis, University of Washington at Seattle (1980)Google Scholar
  2. 2.
    Aczel, P.: Final Universes of Processes. In: Main, M.G., Melton, A.C., Mislove, M.W., Schmidt, D., Brookes, S.D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 1–28. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  3. 3.
    Aczel, P.: A semantic universe for the study of fairness. Very Rough and Incomplete Draft (October 1996)Google Scholar
  4. 4.
    Aczel, P., Mendler, N.P.: A Final Coalgebra Theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  5. 5.
    Adámek, J., Milius, S., Velebil, J.: On coalgebra based on classes. Theoretical Computer Science 316(1-3), 3–23 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Apt, K.R., Olderog, E.-R.: Proof rules and transformations dealing with fairness. Science of Computer Programming 3(1), 65–100 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Baeten, J.C.M.: A brief history of process algebra. Theoretical Computer Science 335(2-3), 131–146 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Barwise, J., Moss, L.: Vicious Circles. Lecture Notes, vol. 60. CLSI (1996)Google Scholar
  9. 9.
    Berger, M.: An interview with Robin Milner (September 2003),
  10. 10.
    Boudol, G., Castellani, I.: Permutation of Transitions: An Event Structure Semantics for CCS and SCCS. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. LNCS, vol. 354, pp. 411–427. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  11. 11.
    Boudol, G., Castellani, I., Hennessy, M., Kiehn, A.: Observing localities. Theoretical Computer Science 114(1), 31–61 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    da Costa, R.J.C., Courtiat, J.-P.: A causality-based semantics for CCS. In: Proceedings of the First North American Process Algebra Workshop, NAPAW 1992, pp. 200–215. Springer, London (1993)Google Scholar
  13. 13.
    Courcoubetis, C., Vardi, M.Y., Wolper, P.: Reasoning about fair concurrent programs. In: Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing, STOC 1986, pp. 283–294. ACM, New York (1986)CrossRefGoogle Scholar
  14. 14.
    Darondeau, P.: About fair asynchrony. Theoretical Computer Science 37, 305–336 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Darondeau, P., Degano, P.: Causal Trees: Interleaving + Causality. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 239–255. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  16. 16.
    Darondeau, P., Kott, L.: On the Observational Semantics of Fair Parallelism. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 147–159. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  17. 17.
    Degano, P., De Nicola, R., Montanari, U.: A partial ordering semantics for CCS. Theoretical Computer Science 75(3), 223–262 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall (1976)Google Scholar
  19. 19.
    Emerson, E.A.: Alternative semantics for temporal logics. Theoretical Computer Science 26(1-2), 121–130 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Emerson, E.A., Halpern, J.Y.: “Sometimes” and “not never” revisited: On branching versus linear time temporal logic. J. ACM 33(1), 151–178 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Peter Gumm, H.: Elements of the general theory of coalgebras. Lecture Notes for LUATCS 1999 at Rand Afrikaans University, Johannesburg, South Africa (1999)Google Scholar
  22. 22.
    Hennessy, M.: Axiomatising finite delay operators. Acta Informatica 21(1), 61–88 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Hennessy, M., Stirling, C.: The power of the future perfect in program logics. Information and Control 67(1-3), 23–52 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Hildebrandt, T.T.: A fully abstract presheaf semantics of SCCS with finite delay. Electronic Notes in Theoretical Computer Science 29, 102–126 (1999)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and System Sciences 3(2), 147–195 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Keller, R.M.: Formal verification of parallel programs. Commun. ACM 19(7), 371–384 (1976)zbMATHCrossRefGoogle Scholar
  28. 28.
    Lamport, L.: “Sometime” is sometimes “not never”: On the temporal logic of programs. In: Proceedings of the 7th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 1980, pp. 174–185. ACM, New York (1980)CrossRefGoogle Scholar
  29. 29.
    Matsikoudis, E., Lee, E.A.: Labelled execution systems. Technical Report UCB/EECS-2012-64, EECS Department, University of California, Berkeley (May 2012)Google Scholar
  30. 30.
    Milner, R.: Synthesis of Communicating Behaviour. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 71–83. Springer, Heidelberg (1978)CrossRefGoogle Scholar
  31. 31.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  32. 32.
    Milner, R.: A finite delay operator in synchronous CCS. Technical Report CSR-116-82, University of Edinburgh (1982)Google Scholar
  33. 33.
    Milner, R.: A calculus of communicating systems. Report ECS-LFCS-86-7, Laboratory for Foundations of Computer Science, Department of Computer Science, University of Edinburgh (August 1986)Google Scholar
  34. 34.
    Milner, R.: Communication and Concurrency. Prentice Hall International Series in Computer Science. Prentice-Hall, Upper Saddle River (1989)zbMATHGoogle Scholar
  35. 35.
    Moore, E.F.: Gedanken-experiments on sequential machines. Automata Studies 34, 129–153 (1956)Google Scholar
  36. 36.
    Park, D.: On the Semantics of Fair Parallelism. In: Bjorner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 504–526. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  37. 37.
    Park, D.: Concurrency and Automata on Infinite Sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  38. 38.
    Plotkin, G.D.: A structural approach to operational semantics (Aarhus notes). Technical Report DAIMI FN–19, Computer Science Department, Aarhus University (September 1981)Google Scholar
  39. 39.
    Plotkin, G.D.: The origins of structural operational semantics. Journal of Logic and Algebraic Programming 60-61, 3–15 (2004)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Pnueli, A.: The Temporal Semantics of Concurrent Programs. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70, pp. 1–20. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  41. 41.
    Pratt, V.R.: Process logic: Preliminary report. In: Proceedings of the 6th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 1979, pp. 93–100. ACM, New York (1979)CrossRefGoogle Scholar
  42. 42.
    Rutten, J.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249(1), 3–80 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Rutten, J., Turi, D.: On the Foundations of Final Semantics: Non-Standard Sets, Metric Spaces, Partial Orders. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1992. LNCS, vol. 666, pp. 477–530. Springer, Heidelberg (1993)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Eleftherios Matsikoudis
    • 1
  • Edward A. Lee
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

Personalised recommendations