Flow Faster: Efficient Decision Algorithms for Probabilistic Simulations

  • Lijun Zhang
  • Holger Hermanns
  • Friedrich Eisenbrand
  • David N. Jansen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4424)

Abstract

Abstraction techniques based on simulation relations have become an important and effective proof technique to avoid the infamous state space explosion problem. In the context of Markov chains, strong and weak simulation relations have been proposed [17,6], together with corresponding decision algorithms [3,5], but it is as yet unclear whether they can be used as effectively as their non-stochastic counterparts. This paper presents drastically improved algorithms to decide whether one (discrete- or continuous-time) Markov chain strongly or weakly simulates another. The key innovation is the use of parametric maximum flow techniques to amortize computations.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Lijun Zhang
    • 1
  • Holger Hermanns
    • 1
  • Friedrich Eisenbrand
    • 2
  • David N. Jansen
    • 3
    • 4
  1. 1.Department of Computer Science, Saarland University, SaarbrückenGermany
  2. 2.Department of Mathematics, University of PaderbornGermany
  3. 3.Department of Computer Science, University of Twente, EnschedeThe Netherlands
  4. 4.Software Modeling and Verification Group, RWTH AachenGermany

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