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General Quantitative Specification Theories with Modalities

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7353)

Abstract

This paper proposes a new theory of quantitative specifications. It generalizes the notions of step-wise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems which arise in system design.

Keywords

  • Transition System
  • Triangle Inequality
  • Structural Composition
  • Label Transition System
  • Trace Distance

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.

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References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide. Springer (2007)

    Google Scholar 

  2. 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)

    CrossRef  Google Scholar 

  3. Bauer, S.S., Juhl, L., Larsen, K.G., Legay, A., Srba, J.: Extending modal transition systems with structured labels. Math. Struct. CS (2012)

    Google Scholar 

  4. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Quantitative analysis of real-time systems using priced timed automata. CACM 54(9), 78–87 (2011)

    Google Scholar 

  5. Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. ACM Trans. Comp. Logic 11(4) (2010)

    Google Scholar 

  6. David, A., Larsen, K.G., Legay, A., Nyman, U., Wąsowski, A.: Timed I/O automata: A complete specification theory for real-time systems. In: HSCC, pp. 91–100. ACM (2010)

    Google Scholar 

  7. de Alfaro, L., Faella, M., Stoelinga, M.: Linear and branching system metrics. IEEE Trans. Soft. Eng. 35(2), 258–273 (2009)

    CrossRef  Google Scholar 

  8. Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Int. J. Game Th. 8, 109–113 (1979)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy Games in Multiweighted Automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 95–115. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  10. Fahrenberg, U., Legay, A., Thrane, C.: The quantitative linear-time–branching-time spectrum. In: FSTTCS. LIPIcs, vol. 13, pp. 103–114 (2011)

    Google Scholar 

  11. Fahrenberg, U., Legay, A., Wąsowski, A.: Vision Paper: Make a Difference! (Semantically). In: Whittle, J., Clark, T., Kühne, T. (eds.) MODELS 2011. LNCS, vol. 6981, pp. 490–500. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  12. Fahrenberg, U., Thrane, C., Larsen, K.G.: Distances for weighted transition systems: Games and properties. In: QAPL. EPTCS, vol. 57, pp. 134–147 (2011)

    Google Scholar 

  13. 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)

    CrossRef  Google Scholar 

  14. 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)

    CrossRef  Google Scholar 

  15. Grumberg, O., Lange, M., Leucker, M., Shoham, S.: Don’t Know in the μ-Calculus. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 233–249. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  16. Henzinger, T.A., Majumdar, R., Prabhu, V.S.: Quantifying Similarities Between Timed Systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 226–241. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  17. Juhl, L., Larsen, K.G., Srba, J.: Modal transition systems with weight intervals. J. Logic Alg. Prog. (2012)

    Google Scholar 

  18. Larsen, K.G.: Modal Specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)

    CrossRef  Google Scholar 

  19. Larsen, K.G., Fahrenberg, U., Thrane, C.: Metrics for weighted transition systems: Axiomatization and complexity. Th. Comp. Sci. 412(28), 3358–3369 (2011)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Munkres, J.R.: Topology. Prentice Hall (2000)

    Google Scholar 

  21. Nyman, U.: Modal Transition Systems as the Basis for Interface Theories and Product Lines. PhD thesis, Aalborg University (September 2008)

    Google Scholar 

  22. Rasmussen, J.I., Larsen, K.G., Subramani, K.: On using priced timed automata to achieve optimal scheduling. Formal Meth. Syst. Design 29(1), 97–114 (2006)

    CrossRef  MATH  Google Scholar 

  23. Thrane, C., Fahrenberg, U., Larsen, K.G.: Quantitative simulations of weighted transition systems. J. Logic Alg. Prog. 79(7), 689–703 (2010)

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. van Breugel, F.: A theory of metric labelled transition systems. Annals of the New York Academy of Sciences 806(1), 69–87 (1996)

    CrossRef  Google Scholar 

  25. van Breugel, F.: A Behavioural Pseudometric for Metric Labelled Transition Systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 141–155. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  26. Zwick, U., Paterson, M.: The Complexity of Mean Payoff Games. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 1–10. Springer, Heidelberg (1995)

    CrossRef  Google Scholar 

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Bauer, S.S., Fahrenberg, U., Legay, A., Thrane, C. (2012). General Quantitative Specification Theories with Modalities. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-30642-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30641-9

  • Online ISBN: 978-3-642-30642-6

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