{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T01:30:26Z","timestamp":1743125426885,"version":"3.40.3"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030995263"},{"type":"electronic","value":"9783030995270"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T00:00:00Z","timestamp":1648598400000},"content-version":"vor","delay-in-days":88,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider turn-based stochastic 2-player games on graphs with<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c9<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-regular winning conditions. We provide a direct symbolic algorithm for solving such games when the winning condition is formulated as a Rabin condition. For a stochastic Rabin game with<jats:italic>k<\/jats:italic>pairs over a game graph with<jats:italic>n<\/jats:italic>vertices, our algorithm runs in<jats:inline-formula><jats:alternatives><jats:tex-math>$$O(n^{k+2}k!)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:msup><mml:mi>n<\/mml:mi><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mi>k<\/mml:mi><mml:mo>!<\/mml:mo><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>symbolic steps, which improves the state of the art.<\/jats:p><jats:p>We have implemented our symbolic algorithm, along with performance optimizations including parallellization and acceleration, in a BDD-based synthesis tool called . We demonstrate the superiority of compared to the state of the art on a set of synthetic benchmarks derived from the VLTS benchmark suite and on a control system benchmark from the literature. In our experiments, performed significantly faster with up to<jats:italic>two<\/jats:italic>orders of magnitude improvement in computation time.<\/jats:p>","DOI":"10.1007\/978-3-030-99527-0_5","type":"book-chapter","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T10:37:21Z","timestamp":1648550241000},"page":"81-98","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Direct Symbolic Algorithm for Solving Stochastic Rabin Games"],"prefix":"10.1007","author":[{"given":"Tamajit","family":"Banerjee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rupak","family":"Majumdar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9864-7475","authenticated-orcid":false,"given":"Kaushik","family":"Mallik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2801-639X","authenticated-orcid":false,"given":"Anne-Kathrin","family":"Schmuck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1922-6678","authenticated-orcid":false,"given":"Sadegh","family":"Soudjani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"de Alfaro, L., Henzinger, T.A., Kupferman, O.: Concurrent reachability games. In: 39th Annual Symposium on Foundations of Computer Science, FOCS. pp. 564\u2013575. IEEE Computer Society (1998)","DOI":"10.1109\/SFCS.1998.743507"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Aminof, B., Ball, T., Kupferman, O.: Reasoning about systems with transition fairness. In: 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning. LNCS, vol. 3452, pp. 194\u2013208. Springer (2004)","DOI":"10.1007\/978-3-540-32275-7_14"},{"key":"5_CR3","unstructured":"Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press (2008)"},{"key":"5_CR4","unstructured":"Banerjee, T., Majumdar, R., Kaushik, M., Schmuck, A.K., Soudjani, S.: Fast symbolic algorithms for omega-regular games under strong transition fairness (2021), https:\/\/www.mpi-sws.org\/tr\/2020-007.pdf"},{"key":"5_CR5","doi-asserted-by":"crossref","unstructured":"Belta, C., Yordanov, B., Gol, E.A.: Formal methods for discrete-time dynamical systems, vol. 15. Springer (2017)","DOI":"10.1007\/978-3-319-50763-7"},{"key":"5_CR6","doi-asserted-by":"crossref","unstructured":"Buchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society 138, 295\u2013311 (1969)","DOI":"10.2307\/1994916"},{"key":"5_CR7","doi-asserted-by":"crossref","unstructured":"Chatterjee, K., de Alfaro, L., Henzinger, T.A.: The complexity of stochastic Rabin and Streett games. In: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP). Lecture Notes in Computer Science, vol. 3580, pp. 878\u2013890. Springer (2005)","DOI":"10.1007\/11523468_71"},{"key":"5_CR8","doi-asserted-by":"crossref","unstructured":"Chatterjee, K., De Alfaro, L., Faella, M., Majumdar, R., Raman, V.: Code aware resource management. Formal Methods in System Design 42(2), 146\u2013174 (2013)","DOI":"10.1007\/s10703-012-0170-4"},{"key":"5_CR9","unstructured":"Chatterjee, K., Jurdzi\u0144ski, M., Henzinger, T.A.: Quantitative stochastic parity games. In: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms. pp. 121\u2013130. Society for Industrial and Applied Mathematics (2004)"},{"key":"5_CR10","unstructured":"Church, A.: Logic, arithmetic, and automata. Proceedings of the International Congress of Mathematicians, 1962 pp. 23\u201335 (1963)"},{"key":"5_CR11","doi-asserted-by":"crossref","unstructured":"van Dijk, T., van de Pol, J.: Sylvan: Multi-core decision diagrams. In: International Conference on Tools and Algorithms for the Construction and Analysis of Systems. pp. 677\u2013691. Springer (2015)","DOI":"10.1007\/978-3-662-46681-0_60"},{"key":"5_CR12","unstructured":"Dutreix, M., Huh, J., Coogan, S.: Abstraction-based synthesis for stochastic systems with omega-regular objectives. arXiv preprint arXiv:2001.09236 (2020)"},{"key":"5_CR13","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs. In: FoCS. vol. 88, pp. 328\u2013337 (1988)","DOI":"10.1109\/SFCS.1988.21949"},{"key":"5_CR14","unstructured":"Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: FoCS. vol. 91, pp. 368\u2013377 (1991)"},{"key":"5_CR15","unstructured":"Garavel, H., Descoubes, N.: Very large transition systems (2003), http:\/\/cadp.inria.fr\/resources\/vlts\/"},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"van Glabbeek, R., H\u00f6fner, P.: Progress, justness, and fairness. ACM Comput. Surv. 52(4) (2019)","DOI":"10.1145\/3329125"},{"key":"5_CR17","doi-asserted-by":"crossref","unstructured":"Gurevich, Y., Harrington, L.: Trees, automata, and games. In: Proceedings of the fourteenth annual ACM symposium on Theory of computing. pp. 60\u201365 (1982)","DOI":"10.1145\/800070.802177"},{"key":"5_CR18","doi-asserted-by":"crossref","unstructured":"Kamgarpour, M., Summers, S., Lygeros, J.: Control design for property specifications on stochastic hybrid systems. Hybrid Systems: Computation and Control pp. 303\u2013312 (April 2013)","DOI":"10.1145\/2461328.2461374"},{"key":"5_CR19","doi-asserted-by":"crossref","unstructured":"Klarlund, N.: Progress measures, immediate determinacy, and a subset construction for tree automata. Annals of Pure and Applied Logic 69(2-3), 243\u2013268 (1994)","DOI":"10.1016\/0168-0072(94)90086-8"},{"key":"5_CR20","doi-asserted-by":"crossref","unstructured":"Kozen, D.: Results on the propositional $$\\mu $$-calculus. Theoretical Computer Science 27(3), 333 \u2013 354 (1983), international Colloquium on Automata, Languages and Programming (ICALP)","DOI":"10.1016\/0304-3975(82)90125-6"},{"key":"5_CR21","doi-asserted-by":"crossref","unstructured":"Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS\u201905). pp. 531\u2013540. IEEE (2005)","DOI":"10.1109\/SFCS.2005.66"},{"key":"5_CR22","doi-asserted-by":"crossref","unstructured":"Laurenti, L., Lahijanian, M., Abate, A., Cardelli, L., Kwiatkowska, M.: Formal and efficient synthesis for continuous-time linear stochastic hybrid processes. IEEE Transactions on Automatic Control (2020)","DOI":"10.1109\/TAC.2020.2975028"},{"key":"5_CR23","doi-asserted-by":"crossref","unstructured":"Long, D.E., Browne, A., Clarke, E.M., Jha, S., Marrero, W.R.: An improved algorithm for the evaluation of fixpoint expressions. In: International Conference on Computer Aided Verification. pp. 338\u2013350. Springer (1994)","DOI":"10.1007\/3-540-58179-0_66"},{"key":"5_CR24","doi-asserted-by":"crossref","unstructured":"Majumdar, R., Mallik, K., Schmuck, A.K., Soudjani, S.: Symbolic qualitative control for stochastic systems via finite parity games. In: ADHS 2021 (2021)","DOI":"10.1016\/j.ifacol.2021.08.486"},{"key":"5_CR25","doi-asserted-by":"crossref","unstructured":"Majumdar, R., Mallik, K., Soudjani, S.: Symbolic controller synthesis for B\u00fcchi specifications on stochastic systems. In: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control. pp. 1\u201311 (2020)","DOI":"10.1145\/3365365.3382214"},{"key":"5_CR26","doi-asserted-by":"crossref","unstructured":"Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Annual Symposium on Theoretical Aspects of Computer Science. pp. 229\u2013242. Springer Berlin Heidelberg (1995)","DOI":"10.1007\/3-540-59042-0_76"},{"key":"5_CR27","doi-asserted-by":"crossref","unstructured":"Piterman, N., Pnueli, A.: Faster solutions of Rabin and Streett games. In: 21st Annual IEEE Symposium on Logic in Computer Science (LICS\u201906). pp. 275\u2013284 (2006)","DOI":"10.1109\/LICS.2006.23"},{"key":"5_CR28","doi-asserted-by":"crossref","unstructured":"Pnueli, A.: On the extremely fair treatment of probabilistic algorithms. In: Proceedings of the fifteenth annual ACM symposium on Theory of computing. pp. 278\u2013290 (1983)","DOI":"10.1145\/800061.808757"},{"key":"5_CR29","doi-asserted-by":"crossref","unstructured":"Pnueli, A., Rosner, R.: A framework for the synthesis of reactive modules. In: Vogt, F.H. (ed.) International Conference on Concurrency, Proceedings. LNCS, vol. 335, pp. 4\u201317. Springer (1988)","DOI":"10.1007\/3-540-50403-6_28"},{"key":"5_CR30","doi-asserted-by":"crossref","unstructured":"Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Annual ACM Symposium on Principles of Programming Languages. pp. 179\u2013190. ACM Press (1989)","DOI":"10.1145\/75277.75293"},{"key":"5_CR31","doi-asserted-by":"crossref","unstructured":"Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society 141, 1\u201335 (1969)","DOI":"10.1090\/S0002-9947-1969-0246760-1"},{"key":"5_CR32","unstructured":"Somenzi, F.: Cudd 3.0.0 (2019), https:\/\/github.com\/ivmai\/cudd"},{"key":"5_CR33","doi-asserted-by":"crossref","unstructured":"Tabuada, P.: Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media (2009)","DOI":"10.1007\/978-1-4419-0224-5"},{"key":"5_CR34","doi-asserted-by":"crossref","unstructured":"Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci. 200(1-2), 135\u2013183 (1998)","DOI":"10.1016\/S0304-3975(98)00009-7"}],"container-title":["Lecture Notes in Computer Science","Tools and Algorithms for the Construction and Analysis of Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-99527-0_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T05:42:00Z","timestamp":1726897320000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-99527-0_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783030995263","9783030995270"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-99527-0_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"30 March 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TACAS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Tools and Algorithms for the Construction and Analysis of Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Munich","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 April 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 April 2022","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":"tacas2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2022\/tacas","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"159","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"46","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"4","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"29% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"10","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report are also included in the proceedings","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}