Parametric and Quantitative Extensions of Modal Transition Systems

  • Uli Fahrenberg
  • Kim Guldstrand Larsen
  • Axel Legay
  • Louis-Marie Traonouez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8415)


Modal transition systems provide a behavioral and compositional specification formalism for reactive systems. We survey two extensions of modal transition systems: parametric modal transition systems for specifications with parameters, and weighted modal transition systems for quantitative specifications.


Model Check Transition System Software Product Line Label Transition System Truth Assignment 
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  1. 1.
    Bauer, S.S., Fahrenberg, U., Juhl, L., Larsen, K.G., Legay, A., Thrane, C.: Quantitative refinement for weighted modal transition systems. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 60–71. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Bauer, S.S., Fahrenberg, U., Legay, A., Thrane, C.: General quantitative specification theories with modalities. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds.) CSR 2012. LNCS, vol. 7353, pp. 18–30. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Bauer, S.S., Juhl, L., Larsen, K.G., Legay, A., Srba, J.: Extending modal transition systems with structured labels. Mathematical Structures in Computer Science 22(4), 581–617 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Beneš, N., Křetínský, J., Larsen, K.G., Møller, M.H., Srba, J.: Parametric modal transition systems. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 275–289. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Beneš, N., Křetínský, J.: Process algebra for modal transition systemses. In: MEMICS. OASICS, vol. 16, pp. 9–18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2010)Google Scholar
  6. 6.
    Boudol, G., Larsen, K.G.: Graphical versus logical specifications. In: Arnold, A. (ed.) CAAP 1990. LNCS, vol. 431, pp. 57–71. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    Černý, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. Theor. Comput. Sci. 413(1), 21–35 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. Theor. Comput. Sci. 345(1), 139–170 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    de Alfaro, L., Faella, M., Stoelinga, M.: Linear and branching system metrics. IEEE Trans. Software Eng. 35(2), 258–273 (2009)CrossRefGoogle Scholar
  10. 10.
    Fahrenberg, U., Legay, A., Thrane, C.: The quantitative linear-time–branching-time spectrum. In: FSTTCS. LIPIcs, vol. 13, pp. 103–114. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)Google Scholar
  11. 11.
    Fahrenberg, U., Legay, A., Traonouez, L.-M.: Specification theories for probabilistic and real-time systems. In: Bensalem, S., Lakhnech, Y., Legay, A. (eds.) FPS 2014 (Sifakis Festschrift). LNCS, vol. 8415, pp. 98–117. Springer, Heidelberg (2014)Google Scholar
  12. 12.
    Fahrenberg, U., Thrane, C.R., Larsen, K.G.: Distances for weighted transition systems: Games and properties. In: QAPL. Electr. Proc. Theor. Comput. Sci., vol. 57, pp. 134–147 (2011)Google Scholar
  13. 13.
    Fecher, H., Schmidt, H.: Comparing disjunctive modal transition systems with an one-selecting variant. J. Logic Alg. Program. 77(1-2), 20–39 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Godefroid, P., Huth, M., Jagadeesan, R.: Abstraction-based model checking using modal transition systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 426–440. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Graf, S., Sifakis, J.: A logic for the description of non-deterministic programs and their properties. Inf. Control 68(1-3), 254–270 (1986)CrossRefGoogle Scholar
  16. 16.
    Gruler, A., Leucker, M., Scheidemann, K.: Modeling and model checking software product lines. In: Barthe, G., de Boer, F.S. (eds.) FMOODS 2008. LNCS, vol. 5051, pp. 113–131. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Holmström, S.: A refinement calculus for specifications in Hennessy-Milner logic with recursion. Formal Asp. Comput. 1(3), 242–272 (1989)CrossRefGoogle Scholar
  18. 18.
    Huth, M., Jagadeesan, R., Schmidt, D.A.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Juhl, L., Larsen, K.G., Srba, J.: Modal transition systems with weight intervals. J. Log. Algebr. Program. 81(4), 408–421 (2012)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Larsen, K.G.: A context dependent equivalence between processes. Theor. Comput. Sci. 49, 184–215 (1987)CrossRefGoogle Scholar
  21. 21.
    Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  22. 22.
    Larsen, K.G., Nyman, U., Wąsowski, A.: On modal refinement and consistency. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 105–119. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, pp. 203–210. IEEE Computer Society (1988)Google Scholar
  24. 24.
    Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS, pp. 108–117. IEEE Computer Society (1990)Google Scholar
  25. 25.
    Mardare, R., Policriti, A.: A complete axiomatic system for a process-based spatial logic. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 491–502. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Nanz, S., Nielson, F., Riis Nielson, H.: Modal abstractions of concurrent behaviour. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 159–173. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  27. 27.
    Raclet, J.-B., Badouel, E., Benveniste, A., Caillaud, B., Passerone, R.: Why are modalities good for interface theories? In: ACSD, pp. 119–127. IEEE (2009)Google Scholar
  28. 28.
    Uchitel, S., Chechik, M.: Merging partial behavioural models. In: FSE, pp. 43–52. ACM (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Uli Fahrenberg
    • 1
  • Kim Guldstrand Larsen
    • 2
  • Axel Legay
    • 1
  • Louis-Marie Traonouez
    • 1
  1. 1.Inria/IRISARennesFrance
  2. 2.Aalborg UniversityAalborgDenmark

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