On the total variation distance of labelled Markov chains

Chen, Taolue and Kiefer, Stefan (2014) On the total variation distance of labelled Markov chains. In: Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS 2014, 14-18 Jul 2014, Vienna, Austria. (doi:10.1145/2603088.2603099)

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Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Article No. 33
Research Areas: A. > School of Science and Technology > Computer Science
Item ID: 16753
Depositing User: Taolue Chen
Date Deposited: 03 Jun 2015 10:30
Last Modified: 12 Jun 2019 16:56
ISBN: 9781450328869
URI: https://eprints.mdx.ac.uk/id/eprint/16753

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