Note: This is an archvied version of our old webpage. Some links might be broken. The current one can be found here.
I7 Logo
Chair for Foundations of Software Reliability and Theoretical Computer Science
Informatik Logo TUM Logo
Publications - On the Total Variation Distance of Labelled Markov Chains


Taolue Chen and Stefan Kiefer. On the total variation distance of labelled Markov chains. Technical report,, 2014. Available at


Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the total variation distance provides a natural measure for the ``inequivalence'' of two LMCs: it is the maximum difference between probabilities that the LMCs assign to the same event. In this paper we develop a theory of the total variation distance between two LMCs, with emphasis on the algorithmic aspects: (1) we provide a polynomial-time algorithm for determining whether two LMCs have distance 1, i.e., whether they can almost always be distinguished; (2) we provide an algorithm for approximating the distance with arbitrary precision; and (3) we show that the threshold problem, i.e., whether the distance exceeds a given threshold, is NP-hard and hard for the square-root-sum problem. We also make a connection between the total variation distance and Bernoulli convolutions.

Suggested BibTeX entry:

    author = {Taolue Chen and Stefan Kiefer},
    institution = {},
    note = {Available at},
    title = {On the Total Variation Distance of Labelled {M}arkov Chains},
    year = {2014}

See ...
Conference version