Automata-Based CSL Model Checking

  • Lijun Zhang
  • David N. Jansen
  • Flemming Nielson
  • Holger Hermanns
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. The presented decision procedure, however, has exponential complexity. In this paper, we propose an effective approximation algorithm for full CSL.

The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. We present a measure-preservation theorem allowing us to reduce the problem to a transient analysis on stratified CTMCs. The corresponding probability can then be approximated in polynomial time (using uniformization). This makes the present work the centerpiece of a broadly applicable full CSL model checker.

Recently, the decision algorithm by Aziz et al. was shown to be incorrect in general. In fact, it works only for stratified CTMCs. As an additional contribution, our measure-preservation theorem can be used to ensure the decidability for general CTMCs.


Markov Chain Model Check Atomic Proposition State Formula Model Check Problem 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lijun Zhang
    • 1
  • David N. Jansen
    • 2
  • Flemming Nielson
    • 1
  • Holger Hermanns
    • 3
  1. 1.DTU InformaticsTechnical University of DenmarkDenmark
  2. 2.Model-based system designRadboud UniversiteitNijmegenThe Netherlands
  3. 3.Computer ScienceSaarland UniversitySaarbrückenGermany

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