{"issue":"11","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"_id":"19669","ec_funded":1,"author":[{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"last_name":"Luo","first_name":"Ruichen","id":"b391db08-1ffe-11ee-8b67-d18ddcfb5a14","full_name":"Luo, Ruichen"},{"last_name":"Saona Urmeneta","first_name":"Raimundo J","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","orcid":"0000-0001-5103-038X","full_name":"Saona Urmeneta, Raimundo J"},{"first_name":"Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","orcid":"0000-0002-1419-3267","full_name":"Svoboda, Jakub"}],"year":"2025","abstract":[{"lang":"eng","text":"We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability condition; (C2) the non-negative coefficients condition; (C3) the sum upto 1 condition; and (C4) the only min or only max operator condition. Several seminal results in the literature focus on special cases. For example, turn-based stochastic games correspond to conditions C2 and C3; and Markov decision process to conditions C2, C3, and C4. However, the systematic computational complexity study of all the cases has not been explored, which we address in this work. Some highlights of our results are: with conditions C2 and C4, and with conditions C3 and C4, the problem is NP-complete, whereas with condition C1 only, the problem is in UP intersects coUP. Finally, we establish the computational complexity of the decision problem of checking the respective conditions."}],"month":"04","article_processing_charge":"No","type":"conference","publication_identifier":{"eissn":["2374-3468"],"issn":["2159-5399"]},"scopus_import":"1","date_created":"2025-05-11T22:02:40Z","project":[{"call_identifier":"H2020","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"external_id":{"arxiv":["2412.12228"]},"corr_author":"1","day":"11","publication":"Proceedings of the 39th AAAI Conference on Artificial Intelligence","publication_status":"published","title":"Linear equations with min and max operators: Computational complexity","acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt) grant and the Austrian Science Fund (FWF) 10.55776/COE12 grant.","oa_version":"Preprint","OA_place":"repository","arxiv":1,"quality_controlled":"1","conference":{"location":"Philadelphia, PA, United States","start_date":"2025-02-25","end_date":"2025-03-04","name":"AAAI: Conference on Artificial Intelligence"},"page":"11150-11157","doi":"10.1609/aaai.v39i11.33212","date_published":"2025-04-11T00:00:00Z","volume":39,"citation":{"ista":"Chatterjee K, Luo R, Saona Urmeneta RJ, Svoboda J. 2025. Linear equations with min and max operators: Computational complexity. Proceedings of the 39th AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 39, 11150–11157.","apa":"Chatterjee, K., Luo, R., Saona Urmeneta, R. J., &#38; Svoboda, J. (2025). Linear equations with min and max operators: Computational complexity. In <i>Proceedings of the 39th AAAI Conference on Artificial Intelligence</i> (Vol. 39, pp. 11150–11157). Philadelphia, PA, United States: Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v39i11.33212\">https://doi.org/10.1609/aaai.v39i11.33212</a>","ieee":"K. Chatterjee, R. Luo, R. J. Saona Urmeneta, and J. Svoboda, “Linear equations with min and max operators: Computational complexity,” in <i>Proceedings of the 39th AAAI Conference on Artificial Intelligence</i>, Philadelphia, PA, United States, 2025, vol. 39, no. 11, pp. 11150–11157.","chicago":"Chatterjee, Krishnendu, Ruichen Luo, Raimundo J Saona Urmeneta, and Jakub Svoboda. “Linear Equations with Min and Max Operators: Computational Complexity.” In <i>Proceedings of the 39th AAAI Conference on Artificial Intelligence</i>, 39:11150–57. Association for the Advancement of Artificial Intelligence, 2025. <a href=\"https://doi.org/10.1609/aaai.v39i11.33212\">https://doi.org/10.1609/aaai.v39i11.33212</a>.","ama":"Chatterjee K, Luo R, Saona Urmeneta RJ, Svoboda J. Linear equations with min and max operators: Computational complexity. In: <i>Proceedings of the 39th AAAI Conference on Artificial Intelligence</i>. Vol 39. Association for the Advancement of Artificial Intelligence; 2025:11150-11157. doi:<a href=\"https://doi.org/10.1609/aaai.v39i11.33212\">10.1609/aaai.v39i11.33212</a>","short":"K. Chatterjee, R. Luo, R.J. Saona Urmeneta, J. Svoboda, in:, Proceedings of the 39th AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2025, pp. 11150–11157.","mla":"Chatterjee, Krishnendu, et al. “Linear Equations with Min and Max Operators: Computational Complexity.” <i>Proceedings of the 39th AAAI Conference on Artificial Intelligence</i>, vol. 39, no. 11, Association for the Advancement of Artificial Intelligence, 2025, pp. 11150–57, doi:<a href=\"https://doi.org/10.1609/aaai.v39i11.33212\">10.1609/aaai.v39i11.33212</a>."},"OA_type":"green","date_updated":"2025-05-12T09:42:09Z","status":"public","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.12228","open_access":"1"}],"publisher":"Association for the Advancement of Artificial Intelligence","intvolume":"        39","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}