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Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth

Asadi, A ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-030-59152-6_14
  3. Publisher: Springer Science and Business Media Deutschland GmbH , 2020
  4. Abstract:
  5. Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in time, given a tree decomposition of the MC with width t. Our results also imply a bound of for each objective on MDPs, where is the number of strategy-iteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on low-treewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experiments show that on low-treewidth MCs and MDPs, our algorithms outperform existing well-established methods by one or more orders of magnitude. © 2020, Springer Nature Switzerland AG
  6. Keywords:
  7. Markov Decision Processes ; Treewidth ; Computational complexity ; Graph algorithms ; Markov chains ; Discrete time Markov chains ; Experimental evaluation ; Hitting probabilities ; Orders of magnitude ; Parameterized algorithm ; Quantitative objectives ; Tree decomposition ; Iterative methods
  8. Source: 18th International Symposium on Automated Technology for Verification and Analysis, ATVA 2020, 19 October 2020 through 23 October 2020 ; Volume 12302 LNCS , 2020 , Pages 253-270
  9. URL: https://link.springer.com/chapter/10.1007/978-3-030-59152-6_14