We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.
This research was funded in part by the European Research Council (ERC) under grant agreement 267989 (QUAREM), the Austrian Science Fund (FWF) under grants project S11402-N23 (RiSE and SHiNE) and Z211-N23 (Wittgenstein Award), by the Czech Science Foundation Grant No. P202/12/G061, and by the SNSF Advanced Postdoc. Mobility Fellowship – grant number P300P2_161067.
CONCUR: Concurrency Theory
Quebec City; Canada
2016-08-23 – 2016-08-26
Daca P, Henzinger TA, Kretinsky J, Petrov T. Linear distances between Markov chains. In: Vol 59. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2016. doi:10.4230/LIPIcs.CONCUR.2016.20
Daca, P., Henzinger, T. A., Kretinsky, J., & Petrov, T. (2016). Linear distances between Markov chains (Vol. 59). Presented at the CONCUR: Concurrency Theory, Quebec City; Canada: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2016.20
Daca, Przemyslaw, Thomas A Henzinger, Jan Kretinsky, and Tatjana Petrov. “Linear Distances between Markov Chains,” Vol. 59. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. https://doi.org/10.4230/LIPIcs.CONCUR.2016.20.
P. Daca, T. A. Henzinger, J. Kretinsky, and T. Petrov, “Linear distances between Markov chains,” presented at the CONCUR: Concurrency Theory, Quebec City; Canada, 2016, vol. 59.
Daca P, Henzinger TA, Kretinsky J, Petrov T. 2016. Linear distances between Markov chains. CONCUR: Concurrency Theory, LIPIcs, vol. 59, 20.
Daca, Przemyslaw, et al. Linear Distances between Markov Chains. Vol. 59, 20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016, doi:10.4230/LIPIcs.CONCUR.2016.20.
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