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: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014, 15-17 Dec 2014, New Delhi, India.

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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

Item Type: Conference or Workshop Item (Paper)
Keywords (uncontrolled): Markovian Models, Entropy, Complexity, Probabilistic Verification
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 16756
Depositing User: Taolue Chen
Date Deposited: 03 Jun 2015 10:56
Last Modified: 09 Sep 2018 09:59
URI: http://eprints.mdx.ac.uk/id/eprint/16756

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