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

Ali Asadi, Krishnendu Chatterjee, Amir Kafshdar Goharshady*, Kiarash Mohammadi, Andreas Pavlogiannis

*Corresponding author for this work

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review


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.

Original languageEnglish
Title of host publicationAutomated Technology for Verification and Analysis - 18th International Symposium, ATVA 2020, Proceedings
EditorsDang Van Hung, Oleg Sokolsky
Number of pages18
Place of publicationCham
Publication date2020
ISBN (Print)978-3-030-59151-9
ISBN (Electronic)978-3-030-59152-6
Publication statusPublished - 2020
EventInternational Symposium on Automated Technology for Verification and Analysis: 18th International Symposium - Hanoi, Viet Nam
Duration: 19 Oct 202023 Oct 2020
Conference number: 18


ConferenceInternational Symposium on Automated Technology for Verification and Analysis
Country/TerritoryViet Nam
SeriesLecture Notes in Computer Science


  • Markov Chains
  • Markov Decision Processes
  • Treewidth

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