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Ratio and Weight Quantiles

  • Daniel Krähmann
  • Jana Schubert
  • Christel Baier
  • Clemens Dubslaff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)

Abstract

Several types of weighted-automata models and formalisms to specify and verify constraints on accumulated weights have been studied in the past. The lack of monotonicity for weight functions with positive and negative values as well as for ratios of the accumulated values of non-negative weight functions renders many verification problems to be undecidable or computationally hard. Our contribution comprises polynomial-time algorithms for computing ratio and weight quantiles in Markov chains, which provide optimal bounds guaranteed almost surely or with positive probability on, e.g., cost-utility ratios or the energy conversion efficiency.

Keywords

Markov Chain Weight Function Polynomial Time Weight Objective Negative Cycle 
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.

Notes

Acknowledgements

We thank Stefan Kiefer for pointing us to the continued-fraction method and its application [20].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Daniel Krähmann
    • 1
  • Jana Schubert
    • 1
  • Christel Baier
    • 1
  • Clemens Dubslaff
    • 1
  1. 1.Faculty of Computer ScienceTechnische Universität DresdenDresdenGermany

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