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An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties

  • Yong Li
  • Wanwei Liu
  • Andrea TurriniEmail author
  • Ernst Moritz Hahn
  • Lijun Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9984)

Abstract

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT solver. The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula. We provide a prototype and show the efficiency of our approach on a number of benchmarks.

Keywords

Markov Chain Model Check Markov Chain Model Product Graph Strongly Connect Component 
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

Acknowledgement

This work is supported by the CDZ project CAP (GZ 1023), by the Chinese Academy of Sciences Fellowship for International Young Scientists, by the National Natural Science Foundation of China (Grants No. 61532019, 61472473, 61550110249, 61550110506, 61103012, 61379054, and 61272335), and by the CAS/SAFEA International Partnership Program for Creative Research Teams.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Yong Li
    • 1
    • 2
  • Wanwei Liu
    • 3
  • Andrea Turrini
    • 1
    Email author
  • Ernst Moritz Hahn
    • 1
  • Lijun Zhang
    • 1
    • 2
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareCASBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.College of Computer ScienceNational University of Defense TechnologyChangshaChina

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