---
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_language: eng
dct_publisher: International Federation of Computational Logic@
dct_title: Algorithms for game metrics@
...