Logical Characterisations and Compositionality of Input-Output Conformance Simulation

  • Luca Aceto
  • Ignacio FábregasEmail author
  • Carlos Gregorio-Rodríguez
  • Anna Ingólfsdóttir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10139)


Input-output conformance simulation Open image in new window has been proposed by Gregorio-Rodríguez, Llana and Martínez-Torres as a simulation-based behavioural preorder underlying model-based testing. This relation is inspired by Tretman’s classic Open image in new window relation, but has better worst-case complexity than Open image in new window and supports stepwise refinement. The goal of this paper is to develop the theory of Open image in new window by studying logical characterisations of this relation and its compositionality. More specifically, this article presents characterisations of Open image in new window in terms of modal logics and compares them with an existing logical characterisation for Open image in new window proposed by Beohar and Mousavi. A precongruence rule format for Open image in new window and a rule format ensuring that operations take quiescence properly into account are also given. Both rule formats are based on the GSOS format by Bloom, Istrail and Meyer.


  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, pp. 197–292. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Benes, N., Daca, P., Henzinger, T.A., Kretínský, J., Nickovic, D., Complete composition operators for IOCO-testing theory. In: Proceedings of the 18th International ACM SIGSOFT Symposium on Component-Based Software Engineering, CBSE, pp. 101–110 (2015)Google Scholar
  3. 3.
    Beohar, H., Mousavi, M.R.: Two logical characterizations for input-output conformance. In: Preproceedings of EXPRESS/SOS 2014 (Short Paper), July 2014Google Scholar
  4. 4.
    Beohar, H., Mousavi, M.R.: A pre-congruence format for \(XY\)-simulation. In: Dastani, M., Sirjani, M. (eds.) FSEN 2015. LNCS, vol. 9392, pp. 215–229. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  5. 5.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    de Frutos-Escrig, D., Gregorio-Rodríguez, C., Palomino, M., Romero-Hernández, D.: Unifying the linear time-branching time spectrum of process semantics. Log. Methods Comput. Sci. 9(2:11), 1–74 (2013)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Fokkink, W., Glabbeek, R.J., Wind, P.: Compositionality of Hennessy-Milner logic by structural operational semantics. Theor. Comput. Sci. 354(3), 421–440 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gregorio-Rodríguez, C., Llana, L., Martínez-Torres, R.: Input-output conformance simulation (iocos) for model based testing. In: Beyer, D., Boreale, M. (eds.) FMOODS/FORTE -2013. LNCS, vol. 7892, pp. 114–129. Springer, Berlin (2013). doi: 10.1007/978-3-642-38592-6_9 CrossRefGoogle Scholar
  9. 9.
    Gregorio-Rodríguez, C., Llana, L., Martínez-Torres, R.: Effectiveness for input output conformance simulation iocos̱. In: Ábrahám, E., Palamidessi, C. (eds.) FORTE 2014. LNCS, vol. 8461, pp. 100–116. Springer, Berlin (2014). doi: 10.1007/978-3-662-43613-4_7 CrossRefGoogle Scholar
  10. 10.
    Gregorio-Rodríguez, C., Llana, L., Martínez-Torres, R.: Extending mCRL2 with ready simulation and iocos input-output conformance simulation. In: Wainwright, R.L., Corchado, J.M., Bechini, A., Hong, J. (eds.) Proceedings of the 30th Annual ACM Symposium on Applied Computing, Salamanca, Spain, 13–17 April 2015, pp. 1781–1788. ACM (2015)Google Scholar
  11. 11.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32, 137–161 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Klin, B., Nachyła, B.: Some undecidable properties of SOS specifications. J. Log. Algebraic Methods Program. (2016).
  13. 13.
    Llana, L., Martínez-Torres, R.: IOCO as a simulation. In: Counsell, S., Núñez, M. (eds.) SEFM 2013. LNCS, vol. 8368, pp. 125–134. Springer, Cham (2014). doi: 10.1007/978-3-319-05032-4_10 CrossRefGoogle Scholar
  14. 14.
    Stokkink, G., Timmer, M., Stoelinga, M., Talking quiescence: a rigorous theory that supports parallelcomposition, action hiding and determinisation. In: Petrenko, A.K., Schlingloff, H. (eds.) MBT. EPTCS, vol. 80, pp. 73–87 (2012)Google Scholar
  15. 15.
    Tretmans, J.: Test generation with inputs, outputs and repetitive quiescence. Softw. Concepts Tools 17(3), 103–120 (1996)zbMATHGoogle Scholar
  16. 16.
    Tretmans, J.: Model Based testing with labelled transition systems. In: Hierons, R.M., Bowen, J.P., Harman, M. (eds.) Formal Methods and Testing. LNCS, vol. 4949, pp. 1–38. Springer, Berlin (2008). doi: 10.1007/978-3-540-78917-8_1 CrossRefGoogle Scholar
  17. 17.
    Bijl, M., Rensink, A., Tretmans, J.: Compositional testing with ioco. In: Petrenko, A., Ulrich, A. (eds.) FATES 2003. LNCS, vol. 2931, pp. 86–100. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    van Glabbeek, R.J.: The linear time -branching time spectrum I: the semantics of concrete, sequential processes. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 3–99. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Luca Aceto
    • 1
  • Ignacio Fábregas
    • 1
    • 2
    Email author
  • Carlos Gregorio-Rodríguez
    • 2
  • Anna Ingólfsdóttir
    • 1
  1. 1.School of Computer Science, ICE-TCSReykjavik UniversityReykjavikIceland
  2. 2.Departamento de Sistemas Informáticos y ComputaciónUniversidad Complutense de MadridMadridSpain

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