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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Abstract
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.
Metadata
Item Type: | Book Section |
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Additional Information: | December 15-17, 2014 - New Delhi, India - ISSN: 1868-8969 |
Keyword(s) / Subject(s): | Markovian Models, Entropy, Complexity, Probabilistic Verification |
School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
Depositing User: | Dr Tingting Han |
Date Deposited: | 02 Dec 2015 13:38 |
Last Modified: | 09 Aug 2023 12:37 |
URI: | https://eprints.bbk.ac.uk/id/eprint/13358 |
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