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    On the complexity of computing maximum entropy for Markovian Models

    Chen, Taolue and Han, Tingting (2014) On the complexity of computing maximum entropy for Markovian Models. In: Raman, V. and Suresh, S.P. (eds.) Proceedings, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings In Informatics 29. Wadern, Germany: Dagstuhl, pp. 571-583. ISBN 9783939897774.

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    We investigate the complexity of computing entropy of various Markovian models including Markov Chains (MCs), Interval Markov Chains (IMCs) and Markov Decision Processes (MDPs). We consider both entropy and entropy rate for general MCs, and study two algorithmic questions, i.e., entropy approximation problem and entropy threshold problem. The former asks for an approximation of the entropy/entropy rate within a given precision, whereas the latter aims to decide whether they exceed a given threshold. We give polynomial-time algorithms for the approximation problem, and show the threshold problem is in P CH3 (hence in PSPACE) and in P assuming some number-theoretic conjectures. Furthermore, we study both questions for IMCs and MDPs where we aim to maximise the entropy/entropy rate among an infinite family of MCs associated with the given model. We give various conditional decidability results for the threshold problem, and show the approximation problem is solvable in polynomial-time via convex programming.


    Item Type: Book Section
    Additional Information: December 15-17, 2014 - New Delhi, India - ISSN: 1868-8969
    Keyword(s) / Subject(s): Markovian Models, Entropy, Complexity, Probabilistic Verification
    School: School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Dr Tingting Han
    Date Deposited: 02 Dec 2015 13:38
    Last Modified: 09 Jun 2021 18:26


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