License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2014.571
URN: urn:nbn:de:0030-drops-48725
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4872/
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Chen, Taolue ; Han, Tingting

On the Complexity of Computing Maximum Entropy for Markovian Models

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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^CH_3 (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.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2014:4872,
  author =	{Taolue Chen and Tingting Han},
  title =	{{On the Complexity of Computing Maximum Entropy for Markovian Models}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{571--583},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4872},
  URN =		{urn:nbn:de:0030-drops-48725},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.571},
  annote =	{Keywords: Markovian Models, Entropy, Complexity, Probabilistic Verification}
}

Keywords: Markovian Models, Entropy, Complexity, Probabilistic Verification
Collection: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 12.12.2014

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