{"citation":{"ieee":"C. Baier, K. Chatterjee, T. Meggendorfer, and J. Piribauer, “Multiplicative rewards in Markovian models,” in <i>2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Singapore, Singapore, 2025, pp. 499–512.","ista":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. 2025. Multiplicative rewards in Markovian models. 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 499–512.","ama":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. Multiplicative rewards in Markovian models. In: <i>2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science</i>. IEEE; 2025:499-512. doi:<a href=\"https://doi.org/10.1109/lics65433.2025.00044\">10.1109/lics65433.2025.00044</a>","apa":"Baier, C., Chatterjee, K., Meggendorfer, T., &#38; Piribauer, J. (2025). Multiplicative rewards in Markovian models. In <i>2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 499–512). Singapore, Singapore: IEEE. <a href=\"https://doi.org/10.1109/lics65433.2025.00044\">https://doi.org/10.1109/lics65433.2025.00044</a>","chicago":"Baier, Christel, Krishnendu Chatterjee, Tobias Meggendorfer, and Jakob Piribauer. “Multiplicative Rewards in Markovian Models.” In <i>2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 499–512. IEEE, 2025. <a href=\"https://doi.org/10.1109/lics65433.2025.00044\">https://doi.org/10.1109/lics65433.2025.00044</a>.","mla":"Baier, Christel, et al. “Multiplicative Rewards in Markovian Models.” <i>2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, IEEE, 2025, pp. 499–512, doi:<a href=\"https://doi.org/10.1109/lics65433.2025.00044\">10.1109/lics65433.2025.00044</a>.","short":"C. Baier, K. Chatterjee, T. Meggendorfer, J. Piribauer, in:, 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2025, pp. 499–512."},"publication_identifier":{"eisbn":["9798331579005"]},"month":"10","title":"Multiplicative rewards in Markovian models","author":[{"last_name":"Baier","full_name":"Baier, Christel","first_name":"Christel"},{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Meggendorfer","full_name":"Meggendorfer, Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","first_name":"Tobias","orcid":"0000-0002-1712-2165"},{"full_name":"Piribauer, Jakob","last_name":"Piribauer","first_name":"Jakob"}],"abstract":[{"lang":"eng","text":"This paper studies the expected value of multiplicative rewards, where rewards obtained in each step are multiplied (instead of the usual addition), in Markov chains (MCs) and Markov decision processes (MDPs). One of the key differences to additive rewards is that the expected value may diverge to ∞ not only due to recurrent, but also due to transient states.For MCs, computing the value is shown to be possible in polynomial time given an oracle for the comparison of succinctly represented integers (CSRI), which is only known to be solvable in polynomial time subject to number-theoretic conjectures. Interestingly, distinguishing whether the value is ∞ or 0 is at least as hard as CSRI, while determining if it is one of these two can be done in polynomial time. In MDPs, the optimal value can be computed in polynomial space. Further refined complexity results and results on the complexity of optimal schedulers are presented. The techniques developed for MDPs additionally allow to solve the multiplicative variant of the stochastic shortest path problem. Finally, for MCs and MDPs where an absorbing state is reached almost surely, all considered problems are solvable in polynomial time."}],"conference":{"location":"Singapore, Singapore","end_date":"2025-06-26","name":"LICS: Logic in Computer Science","start_date":"2025-06-23"},"day":"09","quality_controlled":"1","date_updated":"2025-11-25T07:59:25Z","page":"499-512","acknowledgement":"This work was partly funded by the ERC CoG 863818 (ForM-SMArt), the Austrian Science Fund (FWF) 10.55776/COE12, the DFG Grant 389792660 as part of TRR 248 (Foundations of Perspicuous Software Systems), the Cluster of Excellence EXC 2050/1 (CeTI, project ID\r\n390696704, as part of Germany’s Excellence Strategy), and by the BMBF (Federal Ministry of Education and Research) in DAAD project 57616814 (SECAI, School of Embedded and\r\nComposite AI) as part of the program Konrad Zuse Schools of Excellence in Artificial Intelligence.","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2504.18277"}],"language":[{"iso":"eng"}],"publisher":"IEEE","year":"2025","arxiv":1,"doi":"10.1109/lics65433.2025.00044","_id":"20689","publication":"2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science","article_processing_charge":"No","OA_type":"green","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"}],"date_created":"2025-11-24T14:24:00Z","publication_status":"published","corr_author":"1","department":[{"_id":"KrCh"}],"date_published":"2025-10-09T00:00:00Z","ec_funded":1,"external_id":{"arxiv":["2504.18277"]},"oa":1,"status":"public","scopus_import":"1","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository"}