Quantitative Model Checking Revisited: Neither Decidable Nor Approximable

  • Sergio Giro
  • Pedro R. D’Argenio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4763)


Quantitative model checking computes the probability values of a given property quantifying over all possible schedulers. It turns out that maximum and minimum probabilities calculated in such a way are overestimations on models of distributed systems in which components are loosely coupled and share little information with each other (and hence arbitrary schedulers may result too powerful). Therefore, we focus on the quantitative model checking problem restricted to distributed schedulers that are obtained only as a combination of local schedulers (i.e. the schedulers of each component) and show that this problem is undecidable. In fact, we show that there is no algorithm that can compute an approximation to the maximum probability of reaching a state within a given bound when restricted to distributed schedulers.


Model Check Markov Decision Process Maximum Probability Minimum Probability Maximum Reachability 
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 2007

Authors and Affiliations

  • Sergio Giro
    • 1
  • Pedro R. D’Argenio
    • 1
  1. 1.FaMAF, Universidad Nacional de Córdoba - CONICET, Ciudad Universitaria - 5000 CórdobaArgentina

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