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Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth
, Article 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 ; Chatterjee, K ; Kafshdar Goharshady, A ; Mohammadi, K ; Pavlogiannis, A ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2020
Abstract
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...