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On-the-Fly Exact Computation of Bisimilarity Distances

  • Giorgio Bacci
  • Giovanni Bacci
  • Kim G. Larsen
  • Radu Mardare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7795)

Abstract

This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et. al. at FoSSaCS’12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

Keywords

Markov Chain Discount Factor Transportation Problem Exact Computation Greedy Strategy 
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 2013

Authors and Affiliations

  • Giorgio Bacci
    • 1
    • 2
  • Giovanni Bacci
    • 2
  • Kim G. Larsen
    • 2
  • Radu Mardare
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of UdineItaly
  2. 2.Department of Computer ScienceAalborg UniversityDenmark

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