{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T16:10:54Z","timestamp":1746115854786,"version":"3.40.4"},"publisher-location":"Cham","reference-count":54,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031908965"},{"type":"electronic","value":"9783031908972"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"vor","delay-in-days":120,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We examine two-player games over finite weighted graphs with quantitative (mean-payoff or energy) objective, where one of the players additionally needs to satisfy a fairness objective. The specific fairness we consider is called <jats:italic>strong transition fairness<\/jats:italic>, given by a subset of edges of one of the players, which asks the player to take fair edges infinitely often if their source nodes are visited infinitely often. We show that when fairness is imposed on player\u00a01, these games fall within the class of previously studied <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-regular mean-payoff and energy games. On the other hand, when the fairness is on player\u00a02, to the best of our knowledge, these games have not been previously studied. We provide gadget-based algorithms for fair mean-payoff games where fairness is imposed on either player, and for fair energy games where the fairness is imposed on player\u00a01. For all variants of fair mean-payoff and fair energy (under unknown initial credit) games, we give pseudo-polynomial algorithms to compute the winning regions of both players. Additionally, we analyze the strategy complexities required for these games. Our work is the first to extend the study of strong transition fairness, as well as gadget-based approaches, to the quantitative setting. We thereby demonstrate that the simplicity of strong transition fairness, as well as the applicability of gadget-based techniques, can be leveraged beyond the <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\omega $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c9<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-regular domain.<\/jats:p>","DOI":"10.1007\/978-3-031-90897-2_16","type":"book-chapter","created":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T08:18:30Z","timestamp":1746001110000},"page":"331-354","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fair Quantitative Games"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9462-8514","authenticated-orcid":false,"given":"Ashwani","family":"Anand","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4407-8681","authenticated-orcid":false,"given":"Satya Prakash","family":"Nayak","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1467-1182","authenticated-orcid":false,"given":"Ritam","family":"Raha","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4757-1631","authenticated-orcid":false,"given":"Irmak","family":"Sa\u011flam","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2801-639X","authenticated-orcid":false,"given":"Anne-Kathrin","family":"Schmuck","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,1]]},"reference":[{"doi-asserted-by":"publisher","unstructured":"de\u00a0Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. Theor. Comput. Sci. 345(1), 139\u2013170 (2005). https:\/\/doi.org\/10.1016\/J.TCS.2005.07.033","key":"16_CR1","DOI":"10.1016\/J.TCS.2005.07.033"},{"doi-asserted-by":"publisher","unstructured":"Almagor, S., Boker, U., Kupferman, O.: Formalizing and reasoning about quality. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M.Z., Peleg, D. (eds.) Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Riga, Latvia, July 8-12, 2013, Proceedings, Part II. Lecture Notes in Computer Science, vol.\u00a07966, pp. 15\u201327. Springer (2013). https:\/\/doi.org\/10.1007\/978-3-642-39212-2_3","key":"16_CR2","DOI":"10.1007\/978-3-642-39212-2_3"},{"doi-asserted-by":"publisher","unstructured":"Almagor, S., Kuperberg, D., Kupferman, O.: The sensing cost of monitoring and synthesis. In: Harsha, P., Ramalingam, G. (eds.) 35th IARCS Annual Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2015, December 16-18, 2015, Bangalore, India. LIPIcs, vol.\u00a045, pp. 380\u2013393. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2015). https:\/\/doi.org\/10.4230\/LIPICS.FSTTCS.2015.380","key":"16_CR3","DOI":"10.4230\/LIPICS.FSTTCS.2015.380"},{"doi-asserted-by":"publisher","unstructured":"Almagor, S., Kupferman, O., Velner, Y.: Minimizing expected cost under hard boolean constraints, with applications to quantitative synthesis. In: Desharnais, J., Jagadeesan, R. (eds.) 27th International Conference on Concurrency Theory, CONCUR 2016, August 23-26, 2016, Qu\u00e9bec City, Canada. LIPIcs, vol.\u00a059, pp. 9:1\u20139:15. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2016). https:\/\/doi.org\/10.4230\/LIPICS.CONCUR.2016.9","key":"16_CR4","DOI":"10.4230\/LIPICS.CONCUR.2016.9"},{"unstructured":"Alur, R.: Principles of Cyber-Physical Systems. The MIT Press (2015)","key":"16_CR5"},{"doi-asserted-by":"crossref","unstructured":"Aminof, B., Giacomo, G.D., Rubin, S.: Stochastic fairness and language-theoretic fairness in planning in nondeterministic domains. In: Beck, J.C., Buffet, O., Hoffmann, J., Karpas, E., Sohrabi, S. (eds.) Proceedings of the Thirtieth International Conference on Automated Planning and Scheduling, Nancy, France, October 26-30, 2020. pp. 20\u201328. AAAI Press (2020)","key":"16_CR6","DOI":"10.1609\/icaps.v30i1.6641"},{"doi-asserted-by":"crossref","unstructured":"Amram, G., Maoz, S., Pistiner, O., Ringert, J.O.: Energy mu-calculus: Symbolic fixed-point algorithms for omega-regular energy games. CoRR abs\/2005.00641 (2020)","key":"16_CR7","DOI":"10.1007\/978-3-030-90870-6_9"},{"unstructured":"Anand, A., Nayak, S.P., Raha, R., Sa\u011flam, I., Schmuck, A.K.: Fair quantitative games (2025), https:\/\/arxiv.org\/abs\/2501.17255","key":"16_CR8"},{"doi-asserted-by":"publisher","unstructured":"Asl, H.J., Uchibe, E.: Estimating cost function of expert players in differential games: A model-based method and its data-driven extension. Expert Systems with Applications 255, 124687 (2024). https:\/\/doi.org\/10.1016\/j.eswa.2024.124687","key":"16_CR9","DOI":"10.1016\/j.eswa.2024.124687"},{"unstructured":"Baier, C., Katoen, J.P.: Principles of Model Checking (Representation and Mind Series). The MIT Press (2008)","key":"16_CR10"},{"doi-asserted-by":"crossref","unstructured":"Banerjee, T., Majumdar, R., Mallik, K., Schmuck, A., Soudjani, S.: Fast symbolic algorithms for omega-regular games under strong transition fairness. TheoretiCS 2 (2023)","key":"16_CR11","DOI":"10.46298\/theoretics.23.4"},{"doi-asserted-by":"publisher","unstructured":"Bj\u00f6rklund, H., Sandberg, S., Vorobyov, S.G.: A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games. In: Fiala, J., Koubek, V., Kratochv\u00edl, J. (eds.) Mathematical Foundations of Computer Science 2004, 29th International Symposium, MFCS 2004, Prague, Czech Republic, August 22-27, 2004, Proceedings. Lecture Notes in Computer Science, vol.\u00a03153, pp. 673\u2013685. Springer (2004). https:\/\/doi.org\/10.1007\/978-3-540-28629-5_52","key":"16_CR12","DOI":"10.1007\/978-3-540-28629-5_52"},{"doi-asserted-by":"publisher","unstructured":"Bloem, R., Chatterjee, K., Henzinger, T.A., Jobstmann, B.: Better quality in synthesis through quantitative objectives. In: Bouajjani, A., Maler, O. (eds.) Computer Aided Verification, 21st International Conference, CAV 2009, Grenoble, France, June 26 - July 2, 2009. Proceedings. Lecture Notes in Computer Science, vol.\u00a05643, pp. 140\u2013156. Springer (2009). https:\/\/doi.org\/10.1007\/978-3-642-02658-4_14","key":"16_CR13","DOI":"10.1007\/978-3-642-02658-4_14"},{"doi-asserted-by":"publisher","unstructured":"Bohy, A., Bruy\u00e8re, V., Raskin, J.: Symblicit algorithms for optimal strategy synthesis in monotonic markov decision processes. In: Chatterjee, K., Ehlers, R., Jha, S. (eds.) Proceedings 3rd Workshop on Synthesis, SYNT 2014, Vienna, Austria, July 23-24, 2014. EPTCS, vol.\u00a0157, pp. 51\u201367 (2014). https:\/\/doi.org\/10.4204\/EPTCS.157.8","key":"16_CR14","DOI":"10.4204\/EPTCS.157.8"},{"doi-asserted-by":"publisher","unstructured":"Bouyer, P., Markey, N., Matteplackel, R.M.: Averaging in LTL. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014 - Concurrency Theory - 25th International Conference, CONCUR 2014, Rome, Italy, September 2-5, 2014. Proceedings. Lecture Notes in Computer Science, vol.\u00a08704, pp. 266\u2013280. Springer (2014). https:\/\/doi.org\/10.1007\/978-3-662-44584-6_19","key":"16_CR15","DOI":"10.1007\/978-3-662-44584-6_19"},{"doi-asserted-by":"publisher","unstructured":"Brim, L., Chaloupka, J., Doyen, L., Gentilini, R., Raskin, J.: Faster algorithms for mean-payoff games. Formal Methods Syst. Des. 38(2), 97\u2013118 (2011). https:\/\/doi.org\/10.1007\/S10703-010-0105-X","key":"16_CR16","DOI":"10.1007\/S10703-010-0105-X"},{"doi-asserted-by":"publisher","unstructured":"Bruy\u00e8re, V., Filiot, E., Randour, M., Raskin, J.: Meet your expectations with guarantees: Beyond worst-case synthesis in quantitative games. Inf. Comput. 254, 259\u2013295 (2017). https:\/\/doi.org\/10.1016\/J.IC.2016.10.011","key":"16_CR17","DOI":"10.1016\/J.IC.2016.10.011"},{"doi-asserted-by":"publisher","unstructured":"Chakrabarti, A., de\u00a0Alfaro, L., Henzinger, T.A., Stoelinga, M.: Resource interfaces. In: Alur, R., Lee, I. (eds.) Embedded Software, Third International Conference, EMSOFT 2003, Philadelphia, PA, USA, October 13-15, 2003, Proceedings. Lecture Notes in Computer Science, vol.\u00a02855, pp. 117\u2013133. Springer (2003). https:\/\/doi.org\/10.1007\/978-3-540-45212-6_9","key":"16_CR18","DOI":"10.1007\/978-3-540-45212-6_9"},{"doi-asserted-by":"crossref","unstructured":"Chatterjee, K., de\u00a0Alfaro, L., Faella, M., Majumdar, R., Raman, V.: Code aware resource management. Formal Methods Syst. Des. 42(2), 146\u2013174 (2013)","key":"16_CR19","DOI":"10.1007\/s10703-012-0170-4"},{"doi-asserted-by":"publisher","unstructured":"Chatterjee, K., de\u00a0Alfaro, L., Henzinger, T.A.: The complexity of stochastic rabin and streett games\u2019. In: Automata, Languages and Programming, 32nd International Colloquium, ICALP 2005, Lisbon, Portugal, July 11-15, 2005, Proceedings. Lecture Notes in Computer Science, vol.\u00a03580, pp. 878\u2013890. Springer (2005). https:\/\/doi.org\/10.1007\/11523468_71","key":"16_CR20","DOI":"10.1007\/11523468_71"},{"doi-asserted-by":"crossref","unstructured":"Chatterjee, K., Doyen, L.: Energy parity games. CoRR abs\/1001.5183 (2010)","key":"16_CR21","DOI":"10.1007\/978-3-642-14162-1_50"},{"doi-asserted-by":"publisher","unstructured":"Chatterjee, K., Doyen, L.: Energy and mean-payoff parity markov decision processes. In: Murlak, F., Sankowski, P. (eds.) Mathematical Foundations of Computer Science 2011 - 36th International Symposium, MFCS 2011, Warsaw, Poland, August 22-26, 2011. Proceedings. Lecture Notes in Computer Science, vol.\u00a06907, pp. 206\u2013218. Springer (2011).https:\/\/doi.org\/10.1007\/978-3-642-22993-0_21","key":"16_CR22","DOI":"10.1007\/978-3-642-22993-0_21"},{"doi-asserted-by":"publisher","unstructured":"Chatterjee, K., Doyen, L.: Games and markov decision processes with mean-payoff parity and energy parity objectives. In: Kot\u00e1sek, Z., Bouda, J., Cern\u00e1, I., Sekanina, L., Vojnar, T., Antos, D. (eds.) Mathematical and Engineering Methods in Computer Science - 7th International Doctoral Workshop, MEMICS 2011, Lednice, Czech Republic, October 14-16, 2011, Revised Selected Papers. Lecture Notes in Computer Science, vol.\u00a07119, pp. 37\u201346. Springer (2011). https:\/\/doi.org\/10.1007\/978-3-642-25929-6_3","key":"16_CR23","DOI":"10.1007\/978-3-642-25929-6_3"},{"doi-asserted-by":"publisher","unstructured":"Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Mean-payoff parity games. In: 20th IEEE Symposium on Logic in Computer Science (LICS 2005), 26-29 June 2005, Chicago, IL, USA, Proceedings. pp. 178\u2013187. IEEE Computer Society (2005). https:\/\/doi.org\/10.1109\/LICS.2005.26","key":"16_CR24","DOI":"10.1109\/LICS.2005.26"},{"doi-asserted-by":"crossref","unstructured":"Chatterjee, K., Jurdzinski, M., Henzinger, T.A.: Simple stochastic parity games. In: CSL. Lecture Notes in Computer Science, vol.\u00a02803, pp. 100\u2013113. Springer (2003)","key":"16_CR25","DOI":"10.1007\/978-3-540-45220-1_11"},{"doi-asserted-by":"crossref","unstructured":"Cimatti, A., Pistore, M., Roveri, M., Traverso, P.: Weak, strong, and strong cyclic planning via symbolic model checking. Artif. Intell. 147(1-2), 35\u201384 (2003)","key":"16_CR26","DOI":"10.1016\/S0004-3702(02)00374-0"},{"doi-asserted-by":"publisher","unstructured":"Clemente, L., Raskin, J.: Multidimensional beyond worst-case and almost-sure problems for mean-payoff objectives. In: 30th Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015. pp. 257\u2013268. IEEE Computer Society (2015). https:\/\/doi.org\/10.1109\/LICS.2015.33","key":"16_CR27","DOI":"10.1109\/LICS.2015.33"},{"doi-asserted-by":"publisher","unstructured":"Cole, R., Hariharan, R., Paterson, M., Zwick, U.: Tighter lower bounds on the exact complexity of string matching. SIAM Journal on Computing 24(1), 30\u201345 (1995). https:\/\/doi.org\/10.1137\/S0097539793245829","key":"16_CR28","DOI":"10.1137\/S0097539793245829"},{"doi-asserted-by":"publisher","unstructured":"Comin, C., Rizzi, R.: Improved pseudo-polynomial bound for the value problem and optimal strategy synthesis in mean payoff games. Algorithmica 77(4), 995\u20131021 (Apr 2017). https:\/\/doi.org\/10.1007\/s00453-016-0123-1","key":"16_CR29","DOI":"10.1007\/s00453-016-0123-1"},{"doi-asserted-by":"publisher","unstructured":"Daviaud, L., Jurdzinski, M., Lazic, R.: A pseudo-quasi-polynomial algorithm for mean-payoff parity games. In: Dawar, A., Gr\u00e4del, E. (eds.) Proceedings of the 33rd Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, July 09-12, 2018. pp. 325\u2013334. ACM (2018). https:\/\/doi.org\/10.1145\/3209108.3209162","key":"16_CR30","DOI":"10.1145\/3209108.3209162"},{"doi-asserted-by":"crossref","unstructured":"D\u2019Ippolito, N., Rodr\u00edguez, N., Sardi\u00f1a, S.: Fully observable non-deterministic planning as assumption-based reactive synthesis. J. Artif. Intell. Res. 61, 593\u2013621 (2018)","key":"16_CR31","DOI":"10.1613\/jair.5562"},{"doi-asserted-by":"publisher","unstructured":"Dorfman, D., Kaplan, H., Zwick, U.: A Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games. In: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), vol.\u00a0132, pp. 114:1\u2013114:14. Schloss Dagstuhl\u2013Leibniz-Zentrum fuer Informatik (2019). https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2019.114","key":"16_CR32","DOI":"10.4230\/LIPIcs.ICALP.2019.114"},{"doi-asserted-by":"publisher","unstructured":"Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Int. J. Game Theory 8(2), 109-113 (jun 1979). https:\/\/doi.org\/10.1007\/BF01768705","key":"16_CR33","DOI":"10.1007\/BF01768705"},{"doi-asserted-by":"crossref","unstructured":"Francez, N.: Fairness. Springer, Berlin (1986)","key":"16_CR34","DOI":"10.1007\/978-1-4612-4886-6"},{"doi-asserted-by":"crossref","unstructured":"Hausmann, D., Piterman, N., Saglam, I., Schmuck, A.: Fair \u00f8mega-regular games. In: FoSSaCS (1). Lecture Notes in Computer Science, vol. 14574, pp. 13\u201333. Springer (2024)","key":"16_CR35","DOI":"10.1007\/978-3-031-57228-9_2"},{"doi-asserted-by":"publisher","unstructured":"H\u00e9lou\u00ebt, L., Markey, N., Raha, R.: Reachability games with relaxed energy constraints. In: Leroux, J., Raskin, J. (eds.) Proceedings Tenth International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2019, Bordeaux, France, 2-3rd September 2019. EPTCS, vol.\u00a0305, pp. 17\u201333 (2019). https:\/\/doi.org\/10.4204\/EPTCS.305.2","key":"16_CR36","DOI":"10.4204\/EPTCS.305.2"},{"doi-asserted-by":"crossref","unstructured":"Kress-Gazit, H., Lahijanian, M., Raman, V.: Synthesis for robots: Guarantees and feedback for robot behavior. Annual Review of Control, Robotics, and Autonomous Systems 1(1), 211\u2013236 (2018)","key":"16_CR37","DOI":"10.1146\/annurev-control-060117-104838"},{"doi-asserted-by":"crossref","unstructured":"Majumdar, R., Mallik, K., Schmuck, A., Soudjani, S.: Symbolic control for stochastic systems via parity games. CoRR abs\/2101.00834 (2021)","key":"16_CR38","DOI":"10.1016\/j.ifacol.2021.08.486"},{"doi-asserted-by":"crossref","unstructured":"Martin, D.A.: Borel determinacy. Annals of Mathematics 102(2), 363\u2013371 (1975)","key":"16_CR39","DOI":"10.2307\/1971035"},{"doi-asserted-by":"publisher","unstructured":"Mehdipour, N., Althoff, M., Tebbens, R.D., Belta, C.: Formal methods to comply with rules of the road in autonomous driving: State of the art and grand challenges. Automatica 152, 110692 (2023). https:\/\/doi.org\/10.1016\/j.automatica.2022.110692, https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0005109822005568","key":"16_CR40","DOI":"10.1016\/j.automatica.2022.110692"},{"doi-asserted-by":"publisher","unstructured":"Nilsson, P., Hussien, O., Balkan, A., Chen, Y., Ames, A.D., Grizzle, J.W., Ozay, N., Peng, H., Tabuada, P.: Correct-by-construction adaptive cruise control: Two approaches. IEEE Transactions on Control Systems Technology 24(4), 1294\u20131307 (2016). https:\/\/doi.org\/10.1109\/TCST.2015.2501351","key":"16_CR41","DOI":"10.1109\/TCST.2015.2501351"},{"doi-asserted-by":"crossref","unstructured":"Nilsson, P., Ozay, N., Liu, J.: Augmented finite transition systems as abstractions for control synthesis. Discret. Event Dyn. Syst. 27(2), 301\u2013340 (2017)","key":"16_CR42","DOI":"10.1007\/s10626-017-0243-z"},{"doi-asserted-by":"publisher","unstructured":"Piterman, N., Pnueli, A.: Faster solutions of rabin and streett games. In: 21th IEEE Symposium on Logic in Computer Science (LICS 2006), 12-15 August 2006, Seattle, WA, USA, Proceedings. pp. 275\u2013284. IEEE Computer Society (2006). https:\/\/doi.org\/10.1109\/LICS.2006.23","key":"16_CR43","DOI":"10.1109\/LICS.2006.23"},{"doi-asserted-by":"publisher","unstructured":"Queille, J.P., Sifakis, J.: Fairness and related properties in transition systems \u2013 a temporal logic to deal with fairness. Acta Inf. 19(3), 195\u2013220 (1983). https:\/\/doi.org\/10.1007\/BF00265555","key":"16_CR44","DOI":"10.1007\/BF00265555"},{"unstructured":"Saglam, I., Schmuck, A.: Solving odd-fair parity games. In: FSTTCS. LIPIcs, vol.\u00a0284, pp. 34:1\u201334:24. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2023)","key":"16_CR45"},{"doi-asserted-by":"publisher","unstructured":"Scher, G., Kress-Gazit, H.: Warehouse automation in a day: From model to implementation with provable guarantees. In: 2020 IEEE 16th International Conference on Automation Science and Engineering (CASE). pp. 280\u2013287 (2020). https:\/\/doi.org\/10.1109\/CASE48305.2020.9217012","key":"16_CR46","DOI":"10.1109\/CASE48305.2020.9217012"},{"doi-asserted-by":"crossref","unstructured":"Schmuck, A.K., Thejaswini, K.S., Sa\u011flam, I., Nayak, S.P.: Solving two-player games under progress assumptions. In: Dimitrova, R., Lahav, O., Wolff, S. (eds.) Verification, Model Checking, and Abstract Interpretation. pp. 208\u2013231. Springer Nature Switzerland (2024)","key":"16_CR47","DOI":"10.1007\/978-3-031-50524-9_10"},{"doi-asserted-by":"publisher","unstructured":"Streett, R.S.: Propositional dynamic logic of looping and converse. In: Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing. p. 375-383. STOC \u201981, Association for Computing Machinery (1981). https:\/\/doi.org\/10.1145\/800076.802492","key":"16_CR48","DOI":"10.1145\/800076.802492"},{"unstructured":"Thejaswini, K.S.: Attractor decompositions for solving parity and Rabin games. Ph.D. thesis, Warwick (2023), https:\/\/wrap.warwick.ac.uk\/id\/eprint\/187144\/","key":"16_CR49"},{"doi-asserted-by":"crossref","unstructured":"Thistle, J.G., Malham\u00e9, R.: Control of $$\\omega $$-automata under state fairness assumptions. Systems & control letters 33(4), 265\u2013274 (1998)","key":"16_CR50","DOI":"10.1016\/S0167-6911(97)00106-0"},{"doi-asserted-by":"publisher","unstructured":"Velner, Y., Chatterjee, K., Doyen, L., Henzinger, T.A., Rabinovich, A.M., Raskin, J.: The complexity of multi-mean-payoff and multi-energy games. Inf. Comput. 241, 177\u2013196 (2015). https:\/\/doi.org\/10.1016\/J.IC.2015.03.001","key":"16_CR51","DOI":"10.1016\/J.IC.2015.03.001"},{"doi-asserted-by":"publisher","unstructured":"Wong, K.W., Ehlers, R., Kress-Gazit, H.: Resilient, provably-correct, and high-level robot behaviors. IEEE Transactions on Robotics 34(4), 936\u2013952 (2018). https:\/\/doi.org\/10.1109\/TRO.2018.2830353","key":"16_CR52","DOI":"10.1109\/TRO.2018.2830353"},{"doi-asserted-by":"publisher","unstructured":"Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theor. Comput. Sci. 158(1 &2), 343\u2013359 (1996). https:\/\/doi.org\/10.1016\/0304-3975(95)00188-3","key":"16_CR53","DOI":"10.1016\/0304-3975(95)00188-3"},{"doi-asserted-by":"publisher","unstructured":"Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theoretical Computer Science 158(1), 343\u2013359 (1996). https:\/\/doi.org\/10.1016\/0304-3975(95)00188-3","key":"16_CR54","DOI":"10.1016\/0304-3975(95)00188-3"}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-90897-2_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T08:18:41Z","timestamp":1746001121000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-90897-2_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031908965","9783031908972"],"references-count":54,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-90897-2_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"1 May 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FoSSaCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Foundations of Software Science and Computation Structures","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hamilton, ON","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 May 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 May 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fossacs2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2025\/conferences\/fossacs\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}