[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"year":"2026","main_file_link":[{"url":"https://doi.org/10.1007/s10009-026-00848-y","open_access":"1"}],"OA_place":"publisher","date_published":"2026-03-09T00:00:00Z","quality_controlled":"1","type":"journal_article","_id":"21661","abstract":[{"text":"Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) are key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value iteration; in tool competitions, most participants rely on the latter. These algorithms generally need worst-case exponential time. However, the problem can equally be formulated as a linear programme, solvable in polynomial time. In this paper, we give a detailed overview of today’s state-of-the-art algorithms for MDP model checking with a focus on performance and correctness. We highlight their fundamental differences, and describe various optimizations and implementation variants. We experimentally compare floating-point and exact-arithmetic implementations of all algorithms on three benchmark sets using two probabilistic model checkers. Our results show that (optimistic) value iteration is a sensible default, but other algorithms are preferable in specific settings. This paper thereby provides a guide for MDP verification practitioners—tool builders and users alike.","lang":"eng"}],"language":[{"iso":"eng"}],"citation":{"apa":"Hartmanns, A., Junges, S., Quatmann, T., &#38; Weininger, M. (2026). The revised practitioner’s guide to MDP model checking algorithms. <i>International Journal on Software Tools for Technology Transfer</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10009-026-00848-y\">https://doi.org/10.1007/s10009-026-00848-y</a>","short":"A. Hartmanns, S. Junges, T. Quatmann, M. Weininger, International Journal on Software Tools for Technology Transfer (2026).","ieee":"A. Hartmanns, S. Junges, T. Quatmann, and M. Weininger, “The revised practitioner’s guide to MDP model checking algorithms,” <i>International Journal on Software Tools for Technology Transfer</i>. Springer Nature, 2026.","mla":"Hartmanns, Arnd, et al. “The Revised Practitioner’s Guide to MDP Model Checking Algorithms.” <i>International Journal on Software Tools for Technology Transfer</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s10009-026-00848-y\">10.1007/s10009-026-00848-y</a>.","chicago":"Hartmanns, Arnd, Sebastian Junges, Tim Quatmann, and Maximilian Weininger. “The Revised Practitioner’s Guide to MDP Model Checking Algorithms.” <i>International Journal on Software Tools for Technology Transfer</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s10009-026-00848-y\">https://doi.org/10.1007/s10009-026-00848-y</a>.","ista":"Hartmanns A, Junges S, Quatmann T, Weininger M. 2026. The revised practitioner’s guide to MDP model checking algorithms. International Journal on Software Tools for Technology Transfer.","ama":"Hartmanns A, Junges S, Quatmann T, Weininger M. The revised practitioner’s guide to MDP model checking algorithms. <i>International Journal on Software Tools for Technology Transfer</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s10009-026-00848-y\">10.1007/s10009-026-00848-y</a>"},"day":"09","has_accepted_license":"1","status":"public","scopus_import":"1","ec_funded":1,"publication":"International Journal on Software Tools for Technology Transfer","date_updated":"2026-04-07T09:52:54Z","keyword":["Quantitative model checking","Markov decision process","Linear programming","Value iteration","Policy iteration"],"publication_identifier":{"issn":["1433-2779"],"eissn":["1433-2787"]},"OA_type":"hybrid","oa_version":"Published Version","title":"The revised practitioner’s guide to MDP model checking algorithms","date_created":"2026-04-05T22:01:32Z","publication_status":"epub_ahead","publisher":"Springer Nature","article_processing_charge":"Yes (in subscription journal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"relation":"software","id":"21668","status":"public"}]},"oa":1,"doi":"10.1007/s10009-026-00848-y","acknowledgement":"This research was funded by the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreements 101008233 (MISSION)\r\nand 101034413 (IST-BRIDGE), by the Interreg North Sea project STORM_SAFE, by a KI-Starter grant from the Ministerium für Kultur und Wissenschaft NRW, by NWO VENI grant no. 639.021.754, and by NWO VIDI grant VI.Vidi.223.110 (TruSTy). Experiments were performed with computing resources granted by RWTH Aachen University under project rwth1632.","department":[{"_id":"KrCh"}],"month":"03","project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"article_type":"original","author":[{"full_name":"Hartmanns, Arnd","last_name":"Hartmanns","first_name":"Arnd"},{"full_name":"Junges, Sebastian","last_name":"Junges","first_name":"Sebastian"},{"last_name":"Quatmann","full_name":"Quatmann, Tim","first_name":"Tim"},{"id":"02ab0197-cc70-11ed-ab61-918e71f56881","first_name":"Maximilian","orcid":"0000-0002-0163-2152","full_name":"Weininger, Maximilian","last_name":"Weininger"}]},{"author":[{"last_name":"Fellner","full_name":"Fellner, Andreas","first_name":"Andreas","id":"42BABFB4-F248-11E8-B48F-1D18A9856A87"}],"month":"08","datarep_id":"28","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"project":[{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications"},{"grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering"}],"oa":1,"doi":"10.15479/AT:ISTA:28","related_material":{"record":[{"relation":"popular_science","id":"1603","status":"public"}]},"article_processing_charge":"No","tmp":{"name":"Creative Commons Public Domain Dedication (CC0 1.0)","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","image":"/images/cc_0.png","short":"CC0 (1.0)"},"publisher":"Institute of Science and Technology Austria","file":[{"checksum":"b8bcb43c0893023cda66c1b69c16ac62","file_name":"IST-2015-28-v1+2_Fellner_DataRep.zip","file_id":"5597","date_updated":"2020-07-14T12:47:00Z","creator":"system","relation":"main_file","access_level":"open_access","content_type":"application/zip","file_size":49557109,"date_created":"2018-12-12T13:02:31Z"}],"publist_id":"5564","title":"Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes","date_created":"2018-12-12T12:31:29Z","oa_version":"Published Version","keyword":["Markov Decision Process","Decision Tree","Probabilistic Verification","Counterexample Explanation"],"date_updated":"2025-09-23T08:23:15Z","file_date_updated":"2020-07-14T12:47:00Z","license":"https://creativecommons.org/publicdomain/zero/1.0/","ec_funded":1,"status":"public","citation":{"apa":"Fellner, A. (2015). Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:28\">https://doi.org/10.15479/AT:ISTA:28</a>","mla":"Fellner, Andreas. <i>Experimental Part of CAV 2015 Publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes</i>. Institute of Science and Technology Austria, 2015, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:28\">10.15479/AT:ISTA:28</a>.","ieee":"A. Fellner, “Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.” Institute of Science and Technology Austria, 2015.","short":"A. Fellner, (2015).","chicago":"Fellner, Andreas. “Experimental Part of CAV 2015 Publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.” Institute of Science and Technology Austria, 2015. <a href=\"https://doi.org/10.15479/AT:ISTA:28\">https://doi.org/10.15479/AT:ISTA:28</a>.","ama":"Fellner A. Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes. 2015. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:28\">10.15479/AT:ISTA:28</a>","ista":"Fellner A. 2015. Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:28\">10.15479/AT:ISTA:28</a>."},"day":"13","has_accepted_license":"1","contributor":[{"id":"44CEF464-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Kretinsky"}],"_id":"5549","abstract":[{"lang":"eng","text":"This repository contains the experimental part of the CAV 2015 publication Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.\r\nWe extended the probabilistic model checker PRISM to represent strategies of Markov Decision Processes as Decision Trees.\r\nThe archive contains a java executable version of the extended tool (prism_dectree.jar) together with a few examples of the PRISM benchmark library.\r\nTo execute the program, please have a look at the README.txt, which provides instructions and further information on the archive.\r\nThe archive contains scripts that (if run often enough) reproduces the data presented in the publication."}],"type":"research_data","date_published":"2015-08-13T00:00:00Z","ddc":["004"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015"}]