--- _id: '141' abstract: - lang: eng text: 'Given a model and a specification, the fundamental model-checking problem asks for algorithmic verification of whether the model satisfies the specification. We consider graphs and Markov decision processes (MDPs), which are fundamental models for reactive systems. One of the very basic specifications that arise in verification of reactive systems is the strong fairness (aka Streett) objective. Given different types of requests and corresponding grants, the objective requires that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All ω -regular objectives can be expressed as Streett objectives and hence they are canonical in verification. To handle the state-space explosion, symbolic algorithms are required that operate on a succinct implicit representation of the system rather than explicitly accessing the system. While explicit algorithms for graphs and MDPs with Streett objectives have been widely studied, there has been no improvement of the basic symbolic algorithms. The worst-case numbers of symbolic steps required for the basic symbolic algorithms are as follows: quadratic for graphs and cubic for MDPs. In this work we present the first sub-quadratic symbolic algorithm for graphs with Streett objectives, and our algorithm is sub-quadratic even for MDPs. Based on our algorithmic insights we present an implementation of the new symbolic approach and show that it improves the existing approach on several academic benchmark examples.' acknowledgement: 'Acknowledgements. K. C. and M. H. are partially supported by the Vienna Science and Technology Fund (WWTF) grant ICT15-003. K. C. is partially supported by the Austrian Science Fund (FWF): S11407-N23 (RiSE/SHiNE), and an ERC Start Grant (279307: Graph Games). V. T. is partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie Grant Agreement No. 665385.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Veronika full_name: Loitzenbauer, Veronika last_name: Loitzenbauer - first_name: Simin full_name: Oraee, Simin last_name: Oraee - first_name: Viktor full_name: Toman, Viktor id: 3AF3DA7C-F248-11E8-B48F-1D18A9856A87 last_name: Toman orcid: 0000-0001-9036-063X citation: ama: 'Chatterjee K, Henzinger MH, Loitzenbauer V, Oraee S, Toman V. Symbolic algorithms for graphs and Markov decision processes with fairness objectives. In: Vol 10982. Springer; 2018:178-197. doi:10.1007/978-3-319-96142-2_13' apa: 'Chatterjee, K., Henzinger, M. H., Loitzenbauer, V., Oraee, S., & Toman, V. (2018). Symbolic algorithms for graphs and Markov decision processes with fairness objectives (Vol. 10982, pp. 178–197). Presented at the CAV: Computer Aided Verification, Oxford, United Kingdom: Springer. https://doi.org/10.1007/978-3-319-96142-2_13' chicago: Chatterjee, Krishnendu, Monika H Henzinger, Veronika Loitzenbauer, Simin Oraee, and Viktor Toman. “Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives,” 10982:178–97. Springer, 2018. https://doi.org/10.1007/978-3-319-96142-2_13. ieee: 'K. Chatterjee, M. H. Henzinger, V. Loitzenbauer, S. Oraee, and V. Toman, “Symbolic algorithms for graphs and Markov decision processes with fairness objectives,” presented at the CAV: Computer Aided Verification, Oxford, United Kingdom, 2018, vol. 10982, pp. 178–197.' ista: 'Chatterjee K, Henzinger MH, Loitzenbauer V, Oraee S, Toman V. 2018. Symbolic algorithms for graphs and Markov decision processes with fairness objectives. CAV: Computer Aided Verification, LNCS, vol. 10982, 178–197.' mla: Chatterjee, Krishnendu, et al. Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives. Vol. 10982, Springer, 2018, pp. 178–97, doi:10.1007/978-3-319-96142-2_13. short: K. Chatterjee, M.H. Henzinger, V. Loitzenbauer, S. Oraee, V. Toman, in:, Springer, 2018, pp. 178–197. conference: end_date: 2018-07-17 location: Oxford, United Kingdom name: 'CAV: Computer Aided Verification' start_date: 2018-07-14 date_created: 2018-12-11T11:44:51Z date_published: 2018-07-18T00:00:00Z date_updated: 2023-09-19T09:59:55Z day: '18' ddc: - '000' department: - _id: KrCh doi: 10.1007/978-3-319-96142-2_13 ec_funded: 1 external_id: isi: - '000491469700013' file: - access_level: open_access checksum: 1a6ffa4febe8bb8ac28be3adb3eafebc content_type: application/pdf creator: dernst date_created: 2018-12-18T08:52:38Z date_updated: 2020-07-14T12:44:53Z file_id: '5737' file_name: 2018_LNCS_Chatterjee.pdf file_size: 675606 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 10982' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '07' oa: 1 oa_version: Published Version page: 178-197 project: - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication_status: published publisher: Springer publist_id: '7782' quality_controlled: '1' related_material: record: - id: '10199' relation: dissertation_contains status: public scopus_import: '1' status: public title: Symbolic algorithms for graphs and Markov decision processes with fairness objectives tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10982 year: '2018' ...