On-the-fly computation of bisimilarity distances

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
4 Downloads (Pure)


We propose a distance between continuous-time Markov chains (CTMCs) and study the problem of computing it by comparing three different algorithmic methodologies: iterative, linear program, and on-the-fly. In a work presented at FoSSaCS’12, Chen et al. characterized the bisimilarity distance of Desharnais et al. between discrete-time Markov chains as an optimal solution of a linear program that can be solved by using the ellipsoid method. Inspired by their result, we propose a novel linear program characterization to compute the distance in the continuoustime setting. Differently from previous proposals, ours has a number of constraints that is bounded by a polynomial in the size of the CTMC. This, in particular, proves that the distance we propose can be computed in polynomial time. Despite its theoretical importance, the proposed linear program characterization turns out to be inefficient in practice. Nevertheless, driven by the encouraging results of our previous work presented at TACAS’13, we propose an efficient on-the-fly algorithm, which, unlike the other mentioned solutions, computes the distances between two given states avoiding an exhaustive exploration of the state space. This technique works by successively refining 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 CTMCs show that our algorithm improves, on average, the efficiency of the corresponding iterative and linear program methods with orders of magnitude.

Original languageEnglish
Article number13
Pages (from-to)1-25
Number of pages25
JournalLogical Methods in Computer Science
Issue number2
Publication statusPublished - 30 Jun 2017


  • behavioral distances
  • continuous-time markov chains
  • Markov chains
  • on-the-fly algorithm
  • probabilistic systems


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