{"file":[{"file_name":"2025_LIPIcs_Chatterjee.pdf","creator":"dernst","access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2026-02-18T07:50:56Z","date_updated":"2026-02-18T07:50:56Z","file_id":"21313","checksum":"4477a7fd4fbf0ba6c8e9b15683b5a6b8","file_size":1075724,"relation":"main_file"}],"article_number":"150","citation":{"apa":"Chatterjee, K., Doyen, L., Raskin, J.-F., &#38; Sankur, O. (2025). The value problem for multiple-environment MDPs with parity objective. In <i>52nd International Colloquium on Automata, Languages, and Programming</i>. Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2025.150\">https://doi.org/10.4230/LIPIcs.ICALP.2025.150</a>","ista":"Chatterjee K, Doyen L, Raskin J-F, Sankur O. 2025. The value problem for multiple-environment MDPs with parity objective. 52nd International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming, LIPIcs, , 150.","ieee":"K. Chatterjee, L. Doyen, J.-F. Raskin, and O. Sankur, “The value problem for multiple-environment MDPs with parity objective,” in <i>52nd International Colloquium on Automata, Languages, and Programming</i>, Aarhus, Denmark, 2025.","ama":"Chatterjee K, Doyen L, Raskin J-F, Sankur O. The value problem for multiple-environment MDPs with parity objective. In: <i>52nd International Colloquium on Automata, Languages, and Programming</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2025.150\">10.4230/LIPIcs.ICALP.2025.150</a>","short":"K. Chatterjee, L. Doyen, J.-F. Raskin, O. Sankur, in:, 52nd International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","chicago":"Chatterjee, Krishnendu, Laurent Doyen, Jean-Francois Raskin, and Ocan Sankur. “The Value Problem for Multiple-Environment MDPs with Parity Objective.” In <i>52nd International Colloquium on Automata, Languages, and Programming</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2025.150\">https://doi.org/10.4230/LIPIcs.ICALP.2025.150</a>.","mla":"Chatterjee, Krishnendu, et al. “The Value Problem for Multiple-Environment MDPs with Parity Objective.” <i>52nd International Colloquium on Automata, Languages, and Programming</i>, 150, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2025.150\">10.4230/LIPIcs.ICALP.2025.150</a>."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"arxiv":1,"ddc":["000"],"_id":"21268","language":[{"iso":"eng"}],"month":"07","title":"The value problem for multiple-environment MDPs with parity objective","oa":1,"quality_controlled":"1","acknowledgement":"Krishnendu Chatterjee: ERC CoG 863818 (ForM-SMArt) and Austrian Science Fund\r\n(FWF) 10.55776/COE12. Jean-François Raskin: PDR Weave project FORM-LEARN-POMDP funded by FNRS and DFG, and the support of the Fondation ULB. Ocan Sankur: ANR BisoUS (ANR-22-CE48-0012) and ANR EpiRL (ANR-22-CE23-0029).","status":"public","file_date_updated":"2026-02-18T07:50:56Z","date_published":"2025-07-30T00:00:00Z","OA_place":"publisher","OA_type":"gold","abstract":[{"text":"We consider multiple-environment Markov decision processes (MEMDP), which consist of a finite set of MDPs over the same state space, representing different scenarios of transition structure and probability. The value of a strategy is the probability to satisfy the objective, here a parity objective, in the worst-case scenario, and the value of an MEMDP is the supremum of the values achievable by a strategy.\r\nWe show that deciding whether the value is 1 is a PSPACE-complete problem, and even in P when the number of environments is fixed, along with new insights to the almost-sure winning problem, which is to decide if there exists a strategy with value 1. Pure strategies are sufficient for theses problems, whereas randomization is necessary in general when the value is smaller than 1. We present an algorithm to approximate the value, running in double exponential space. Our results are in contrast to the related model of partially-observable MDPs where all these problems are known to be undecidable.","lang":"eng"}],"conference":{"name":"ICALP: Automata, Languages and Programming","location":"Aarhus, Denmark","start_date":"2025-07-08","end_date":"2025-07-11"},"date_created":"2026-02-17T07:49:17Z","department":[{"_id":"KrCh"}],"date_updated":"2026-02-18T07:53:26Z","publication_status":"published","scopus_import":"1","publication_identifier":{"isbn":["9783959773720"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"},{"full_name":"Doyen, Laurent","first_name":"Laurent","last_name":"Doyen"},{"last_name":"Raskin","first_name":"Jean-Francois","full_name":"Raskin, Jean-Francois"},{"full_name":"Sankur, Ocan","last_name":"Sankur","first_name":"Ocan"}],"day":"30","publication":"52nd International Colloquium on Automata, Languages, and Programming","doi":"10.4230/LIPIcs.ICALP.2025.150","type":"conference","article_processing_charge":"No","year":"2025","has_accepted_license":"1","corr_author":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa_version":"Published Version","alternative_title":["LIPIcs"],"external_id":{"arxiv":["2504.15960"]},"ec_funded":1}