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More or Less True DCTL for Continuous-Time MDPs

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Formal Modeling and Analysis of Timed Systems (FORMATS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8053))

Abstract

Discounted Computation Tree Logic is a logic that measures utility (as a real value in the interval [0,1]) instead of discrete truth (only 0 or 1). It is able to express properties that give more weight to the near future than to the far future. This article extends earlier work on DCTL with time, to continuous-time Markov chains and continuous-time Markov decision processes. It presents model checking algorithms for the two possible semantics of DCTL.

A long version of this article containing full proofs is available as [4].

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References

  1. de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. Theoretical Computer Science 345(1), 139–170 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baier, C., Cloth, L., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Performability assessment by model checking of Markov reward models. Formal Methods in System Design 36(1), 1–36 (2010)

    Article  MATH  Google Scholar 

  3. Baier, C., Hermanns, H., Katoen, J.-P., Haverkort, B.R.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time Markov decision processes. Theoretical Computer Science 345(1), 2–26 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jansen, D.N.: More or less true: DCTL for continuous-time MDPs. Tech. Rep. ICIS–R13006, Radboud Universiteit, Nijmegen (2013), http://www.cs.ru.nl/research/reports

  5. Maplesoft: technical computing software for engineers, mathematicians, scientists, instructors and students, http://www.maplesoft.com/

  6. Neuhäußer, M.R., Stoelinga, M., Katoen, J.-P.: Delayed nondeterminism in continuous-time Markov decision processes. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 364–379. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Wolovick, N., Johr, S.: A characterization of meaningful schedulers for continuous-time Markov decision processes. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 352–367. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Zadeh, L.A.: Fuzzy sets, fuzzy logic, and fuzzy systems. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  9. Zhang, L., Jansen, D.N., Nielson, F., Hermanns, H.: Efficient CSL model checking using stratification. Logical Methods in Computer Science 8(2), paper 17 (2012)

    Google Scholar 

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Jansen, D.N. (2013). More or Less True DCTL for Continuous-Time MDPs. In: Braberman, V., Fribourg, L. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2013. Lecture Notes in Computer Science, vol 8053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40229-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-40229-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40228-9

  • Online ISBN: 978-3-642-40229-6

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