---
res:
  bibo_abstract:
  - Simulation and bisimulation metrics for stochastic systems provide a quantitative
    generalization of the classical simulation and bisimulation relations. These metrics
    capture the similarity of states with respect to quantitative specifications written
    in the quantitative mu-calculus and related probabilistic logics. We first show
    that the metrics provide a bound for the difference in long-run average and discounted
    average behavior across states, indicating that the metrics can be used both in
    system verification, and in performance evaluation. For turn-based games and MDPs,
    we provide a polynomial-time algorithm for the computation of the one-step metric
    distance between states. The algorithm is based on linear programming; it improves
    on the previous known exponential-time algorithm based on a reduction to the theory
    of reals. We then present PSPACE algorithms for both the decision problem and
    the problem of approximating the metric distance between two states, matching
    the best known algorithms for Markov chains. For the bisimulation kernel of the
    metric our algorithm works in time O(n(4)) for both turn-based games and MDPs;
    improving the previously best known O(n(9).log(n)) time algorithm for MDPs. For
    a concurrent game G, we show that computing the exact distance be tween states
    is at least as hard as computing the value of concurrent reachability games and
    the square-root-sum problem in computational geometry. We show that checking whether
    the metric distance is bounded by a rational r, can be done via a reduction to
    the theory of real closed fields, involving a formula with three quantifier alternations,
    yielding O(vertical bar G vertical bar(O(vertical bar G vertical bar 5))) time
    complexity, improving the previously known reduction, which yielded O(vertical
    bar G vertical bar(O(vertical bar G vertical bar 7))) time complexity. These algorithms
    can be iterated to approximate the metrics using binary search@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Krishnendu
      foaf_name: Chatterjee, Krishnendu
      foaf_surname: Chatterjee
      foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4561-241X
  - foaf_Person:
      foaf_givenName: Luca
      foaf_name: De Alfaro, Luca
      foaf_surname: De Alfaro
  - foaf_Person:
      foaf_givenName: Ritankar
      foaf_name: Majumdar, Ritankar
      foaf_surname: Majumdar
  - foaf_Person:
      foaf_givenName: Vishwanath
      foaf_name: Raman, Vishwanath
      foaf_surname: Raman
  bibo_doi: 10.2168/LMCS-6(3:13)2010
  bibo_issue: '3'
  bibo_volume: 6
  dct_date: 2010^xs_gYear
  dct_identifier:
  - UT:000282653500013
  dct_language: eng
  dct_publisher: International Federation of Computational Logic@
  dct_title: Algorithms for game metrics@
...