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.
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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)
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)
Almagor, S., Boker, U., Kupferman, O.: Discounting in LTL. Research Report 1406.4249, arXiv, 21 pages (2014)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
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)
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)
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)
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)
Bollig, B., Decker, N., Leucker, M.: Frequency linear-time temporal logic. In: TASE 2012, pp. 85–92. IEEE Comp. Soc. Press (2012)
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)
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)
Černý, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. Theor. Computer Science 413(1), 21–35 (2012)
Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. ACM Transactions on Computational Logic 11(4) (2010)
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)
Doyen, L.: Games and Automata: From Boolean to Quantitative Verification. Mémoire d’habilitation, ENS Cachan, France (2012)
Droste, M., Kuich, W., Vogler, W. (eds.): Handbook of Weighted Automata. Springer (2009)
Faella, M., Legay, A., Stoelinga, M.: Model checking quantitative linear time logic. In: QAPL 2008. ENTCS, vol. 220, pp. 61–77. Elsevier Science (2008)
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)
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)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Inc. (1967)
Schützenberger, M.-P.: On the definition of a family of automata. Information and Control 4(2-3), 245–270 (1961)
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)
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Bouyer, P., Markey, N., Matteplackel, R.M. (2014). Averaging in LTL . In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_19
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DOI: https://doi.org/10.1007/978-3-662-44584-6_19
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