Probabilistic CTL\(^{*}\): The Deductive Way

  • Rayna Dimitrova
  • Luis María Ferrer Fioriti
  • Holger Hermanns
  • Rupak Majumdar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)

Abstract

Complex probabilistic temporal behaviours need to be guaranteed in robotics and various other control domains, as well as in the context of families of randomized protocols. At its core, this entails checking infinite-state probabilistic systems with respect to quantitative properties specified in probabilistic temporal logics. Model checking methods are not directly applicable to infinite-state systems, and techniques for infinite-state probabilistic systems are limited in terms of the specifications they can handle.

This paper presents a deductive approach to the verification of countable-state systems against properties specified in probabilistic CTL\(^{*}\), on models featuring both nondeterministic and probabilistic choices. The deductive proof system we propose lifts the classical proof system by Kesten and Pnueli to the probabilistic setting. However, the soundness arguments are completely distinct and go via the theory of martingales. Completeness results for the finite-state case and an infinite-state example illustrate the effectiveness of our approach.

Notes

Acknowledgements

This work is supported by the EU FP7 projects 295261 (MEALS) and 318490 (SENSATION), by the DFG Transregional Collaborative Research Centre SFB/TR 14 AVACS, and by the CDZ project 1023 (CAP).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Rayna Dimitrova
    • 1
  • Luis María Ferrer Fioriti
    • 2
  • Holger Hermanns
    • 2
  • Rupak Majumdar
    • 1
  1. 1.MPI-SWSKaiserslautern and SaarbrückenGermany
  2. 2.Saarland UniversitySaarbrückenGermany

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