BIROn - Birkbeck Institutional Research Online

    On the total variation distance of labelled Markov chains

    Chen, Taolue and Kiefer, S. (2014) On the total variation distance of labelled Markov chains. In: UNSPECIFIED (ed.) CSL-LICS '14 Proceedings of the 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). New York, U.S.: ACM, 33:1-33:10. ISBN 9781450328869.

    Full text not available from this repository.

    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.

    Metadata

    Item Type: Book Section
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Dr Taolue Chen
    Date Deposited: 27 Sep 2017 11:18
    Last Modified: 27 Sep 2017 11:18
    URI: http://eprints.bbk.ac.uk/id/eprint/19660

    Statistics

    Downloads
    Activity Overview
    0Downloads
    75Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item