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Averaging in LTL

  • Patricia Bouyer
  • Nicolas Markey
  • Raj Mohan Matteplackel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8704)

Abstract

For the accurate analysis of computerized systems, powerful quantitative formalisms have been designed, together with efficient verification algorithms. However, verification has mostly remained boolean — either a property is true, or it is false. We believe that this is too crude in a context where quantitative information and constraints are crucial: correctness should be quantified!

In a recent line of works, several authors have proposed quantitative semantics for temporal logics, using e.g. discounting modalities (which give less importance to distant events). In the present paper, we define and study a quantitative semantics of LTL with averaging modalities, either on the long run or within an until modality. This, in a way, relaxes the classical Boolean semantics of LTL, and provides a measure of certain properties of a model. We prove that computing and even approximating the value of a formula in this logic is undecidable.

Keywords

Model Check Temporal Logic Atomic Proposition Kripke Structure Counter Machine 
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. 1.
    Almagor, S., Boker, U., Kupferman, O.: Formalizing and reasoning about quality. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 15–27. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Almagor, S., Boker, U., Kupferman, O.: Discounting in LTL (To appear). In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 424–439. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  3. 3.
    Almagor, S., Boker, U., Kupferman, O.: Discounting in LTL. Research Report 1406.4249, arXiv, 21 pages (2014)Google Scholar
  4. 4.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)Google Scholar
  6. 6.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.K.: Model-checking continuous-time Markov chains. ACM Transactions on Computational Logic 1(1), 162–170 (2000)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Boker, U., Chatterjee, K., Henzinger, T.A., Kupferman, O.: Temporal specifications with accumulative values. In: LICS 2011, pp. 43–52. IEEE Comp. Soc. Press (2011)Google Scholar
  9. 9.
    Bollig, B., Decker, N., Leucker, M.: Frequency linear-time temporal logic. In: TASE 2012, pp. 85–92. IEEE Comp. Soc. Press (2012)Google Scholar
  10. 10.
    Bouyer, P., Gardy, P., Markey, N.: Quantitative verification of weighted kripke structures. Research Report LSV-14-08, Laboratoire Spécification et Vérification, ENS Cachan, France, 26 pages (2014)Google Scholar
  11. 11.
    Bouyer, P., Markey, N., Matteplackel, R.M.: Quantitative verification of weighted kripke structures. Research Report LSV-14-02, Laboratoire Spécification et Vérification, ENS Cachan, France, 35 pages (2014)Google Scholar
  12. 12.
    Černý, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. Theor. Computer Science 413(1), 21–35 (2012)CrossRefzbMATHGoogle Scholar
  13. 13.
    Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. ACM Transactions on Computational Logic 11(4) (2010)Google Scholar
  14. 14.
    de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. Theor. Computer Science 345(1), 139–170 (2005)CrossRefzbMATHGoogle Scholar
  15. 15.
    Doyen, L.: Games and Automata: From Boolean to Quantitative Verification. Mémoire d’habilitation, ENS Cachan, France (2012)Google Scholar
  16. 16.
    Droste, M., Kuich, W., Vogler, W. (eds.): Handbook of Weighted Automata. Springer (2009)Google Scholar
  17. 17.
    Faella, M., Legay, A., Stoelinga, M.: Model checking quantitative linear time logic. In: QAPL 2008. ENTCS, vol. 220, pp. 61–77. Elsevier Science (2008)Google Scholar
  18. 18.
    Henzinger, T.A.: Quantitative reactive models. In: France, R.B., Kazmeier, J., Breu, R., Atkinson, C. (eds.) MODELS 2012. LNCS, vol. 7590, pp. 1–2. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  19. 19.
    Henzinger, T.A., Otop, J.: From model checking to model measuring. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 273–287. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Inc. (1967)Google Scholar
  21. 21.
    Schützenberger, M.-P.: On the definition of a family of automata. Information and Control 4(2-3), 245–270 (1961)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Tomita, T., Hiura, S., Hagihara, S., Yonezaki, N.: A temporal logic with mean-payoff constraints. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 249–265. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Nicolas Markey
    • 1
  • Raj Mohan Matteplackel
    • 1
  1. 1.LSV – CNRS and ENS CachanFrance

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