Acta Informatica

, Volume 52, Issue 2–3, pp 207–234 | Cite as

On constructibility and unconstructibility of LTS operators from other LTS operators

  • Antti ValmariEmail author
Original Article


An LTS operator can be constructed from a set of LTS operators up to an equivalence if and only if there is an LTS expression that only contains operators from the set and whose result is equivalent to the result of the operator. In this publication this idea is made precise in the context where each LTS has an alphabet of its own and the operators may depend on the alphabets. Then the extent to which LTS operators are constructible is studied. Most, if not all, established LTS operators have the property that each trace of the result arises from the execution of no more than one trace of each of its argument LTSs, and similarly for infinite traces. All LTS operators that have this property and satisfy some other rather weak regularity properties can be constructed from parallel composition and hiding up to the equivalence that compares the alphabets, traces, and infinite traces of the LTSs. Furthermore, a collection of other miscellaneous constructibility and unconstructibility results is presented.

Mathematics Subject Classification




I thank Walter Vogler for the helpful discussions on “\(\approx _{{\mathsf {shd}}}\)” and other topics that we have had every now and then. I also thank the anonymous reviewers for their valuable comments, written in a very helpful way, on related work and other issues.


  1. 1.
    Aceto, L., Fokkink, W.J., Verhoef, C.: Structural operational semantics. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, Chapter 3, pp. 197–292. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Arnold, A.: Finite Transition Systems. Prentice-Hall, Englewood Cliffs (1994)zbMATHGoogle Scholar
  3. 3.
    Austry, D., Boudol, G.: Algèbre de Processus et Synchronisation. Theoret. Comput. Sci. 30, 91–131 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bloom, B.: Structural operational semantics for weak bisimulations. Theoret. Comput. Sci. 146(1&2), 25–68 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Bolognesi, T., Brinksma, E.: Introduction to the ISO Specification Language LOTOS. Comput. Netw. ISDN Syst. 14, 25–59 (1987)CrossRefGoogle Scholar
  6. 6.
    Boudol, G.: Notes on algebraic calculi of processes. In: Apt, K. (ed.) Logics and Models of Concurrent Systems, NATO ASI Series F13, pp. 261–303. Springer, Berlin (1985)CrossRefGoogle Scholar
  7. 7.
    de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theoret. Comput. Sci. 37, 245–267 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gibson-Robinson, T.: Efficient simulation of CSP-like languages. In: Welch, P.H., Barnes, F.R.M., Broenink, J.F., Chalmers, K., Pedersen, J.B., Sampson, A.T. (eds.) Communicating Process Architectures 2013, pp. 185–204. Open Channel Publishing Ltd., Bicester (2013)Google Scholar
  9. 9.
    Gorla, D.: Towards a unified approach to encodability and separation results for process calculi. Inf. Comput. 208(9), 1031–1053 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Kaivola, R., Valmari, A.: The weakest compositional semantic equivalence preserving nexttime-less linear temporal logic. In: Cleaveland, R. (ed.) CONCUR ’92, Third International Conference on Concurrency Theory, Lecture Notes in Computer Science, vol. 630, pp. 207–221 (1992)Google Scholar
  11. 11.
    Karsisto, K.: A new parallel composition operator for verification tools. Dr.Tech. Thesis, Tampere University of Technology Publications 420, Tampere, Finland (2003)Google Scholar
  12. 12.
    Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems, Volume I: Specification. Springer, Berlin (1992)CrossRefGoogle Scholar
  13. 13.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  14. 14.
    Rensink, A., Vogler, W.: Fair testing. Inf. Comput. 205, 125–198 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Roscoe, A.W.: Understanding Concurrent Systems. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Valmari, A.: Failure-based equivalences are faster than many believe. In: Desel, J. (ed.) Structures in Concurrency Theory 1995, Springer-Verlag Workshops in Computing Series, pp. 326–340 (1995)Google Scholar
  17. 17.
    Valmari, A.: The weakest deadlock-preserving congruence. Inf. Process. Lett. 53, 341–346 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Valmari, A.: Stubborn set methods for process algebras. In: Peled, D.A., Pratt, V.R., Holzmann, G.J. (eds.) Partial Order Methods in Verification: DIMACS Workshop, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 29, pp. 213–231. American Mathematical Society (1997)Google Scholar
  19. 19.
    Valmari, A.: A Chaos-free failures divergences semantics with applications to verification. In: Davies, J., Roscoe, B., Woodcock, J. (eds.) Millennial Perspectives in Computer Science, Proceedings of the 1999 Oxford-Microsoft Symposium in Honour of sir Tony Hoare, Palgrave, pp. 365–382 (2000)Google Scholar
  20. 20.
    Valmari, A.: All linear-time congruences for familiar operators. Log. Methods Comput. Sci. 9(11), 1–34 (2013)MathSciNetGoogle Scholar
  21. 21.
    Valmari, A., Tienari, M.: Compositional failure-based semantic models for basic LOTOS. Formal Aspects Comput. 7(4), 440–468 (1995)CrossRefzbMATHGoogle Scholar
  22. 22.
    van Glabbeek, R.: On cool congruence formats for weak bisimulations. Theoret. Comput. Sci. 412(28), 3283–3302 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    van Glabbeek, R.: Musings on encodings and expressiveness. In: Luttik, B., Reniers, M.A. (eds.) Proceedings of Combined 19th International Workshop on Expressiveness in Concurrency and 9th Workshop on Structured Operational Semantics, Electronic Proceedings in Theoretical Computer Science, vol. 89, pp. 81–98 (2012)Google Scholar
  24. 24.
    van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics (Extended Abstract). In: Ritter, G. (ed.) Proceedings of IFIP International Conference on Information Processing ’89, pp. 613–618. North-Holland (1989)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsTampere University of TechnologyTampereFinland

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