{"alternative_title":["Proceedings Symposium on Logic in Computer Science"],"_id":"1140","conference":{"end_date":"2016-07-08","start_date":"2016-07-05","location":"New York, NY, USA","name":"LICS: Logic in Computer Science"},"author":[{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"last_name":"Dvoák","full_name":"Dvoák, Wolfgang","first_name":"Wolfgang"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","first_name":"Monika H","full_name":"Henzinger, Monika H"},{"first_name":"Veronika","full_name":"Loitzenbauer, Veronika","last_name":"Loitzenbauer"}],"doi":"10.1145/2933575.2935304","abstract":[{"lang":"eng","text":"Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to several fundamental -regular objectives, e.g., Rabin and Streett objectives. For many of these problems the best-known upper bounds are quadratic or cubic, yet no super-linear lower bounds are known. In this work our contributions are two-fold: First, we present several improved algorithms, and second, we present the first conditional super-linear lower bounds based on widely believed assumptions about the complexity of CNF-SAT and combinatorial Boolean matrix multiplication. A separation result for two models with respect to an objective means a conditional lower bound for one model that is strictly higher than the existing upper bound for the other model, and similarly for two objectives with respect to a model. Our results establish the following separation results: (1) A separation of models (graphs and MDPs) for disjunctive queries of reachability and Büchi objectives. (2) Two kinds of separations of objectives, both for graphs and MDPs, namely, (2a) the separation of dual objectives such as Streett/Rabin objectives, and (2b) the separation of conjunction and disjunction of multiple objectives of the same type such as safety, Büchi, and coBüchi. In summary, our results establish the first model and objective separation results for graphs and MDPs for various classical -regular objectives. Quite strikingly, we establish conditional lower bounds for the disjunction of objectives that are strictly higher than the existing upper bounds for the conjunction of the same objectives. © 2016 ACM."}],"publication_status":"published","publication":"Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science","type":"conference","date_updated":"2022-09-09T11:46:17Z","external_id":{"arxiv":["1602.02670"]},"status":"public","project":[{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23","call_identifier":"FWF","name":"Rigorous Systems Engineering"},{"name":"Efficient Algorithms for Computer Aided Verification","_id":"25892FC0-B435-11E9-9278-68D0E5697425","grant_number":"ICT15-003"}],"page":"197 - 206","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"K.  C.,  M.  H.,  and  W.  D.  are  partially  supported  by  the  Vienna\r\nScience and Technology Fund (WWTF) through project ICT15-003.\r\nK. C. is partially supported by the Austrian Science Fund (FWF)\r\nNFN Grant No S11407-N23 (RiSE/SHiNE) and an ERC Start grant\r\n(279307: Graph Games). For W. D., M. H., and V. L. the research\r\nleading to these results has received funding from the European\r\nResearch Council under the European Union’s Seventh Framework\r\nProgramme (FP/2007-2013) / ERC Grant Agreement no. 340506.","department":[{"_id":"KrCh"}],"article_processing_charge":"No","month":"07","date_created":"2018-12-11T11:50:22Z","citation":{"short":"K. Chatterjee, W. Dvoák, M.H. Henzinger, V. Loitzenbauer, in:, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2016, pp. 197–206.","ama":"Chatterjee K, Dvoák W, Henzinger MH, Loitzenbauer V. Model and objective separation with conditional lower bounds: disjunction is harder than conjunction. In: <i>Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science</i>. IEEE; 2016:197-206. doi:<a href=\"https://doi.org/10.1145/2933575.2935304\">10.1145/2933575.2935304</a>","mla":"Chatterjee, Krishnendu, et al. “Model and Objective Separation with Conditional Lower Bounds: Disjunction Is Harder than Conjunction.” <i>Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science</i>, IEEE, 2016, pp. 197–206, doi:<a href=\"https://doi.org/10.1145/2933575.2935304\">10.1145/2933575.2935304</a>.","ieee":"K. Chatterjee, W. Dvoák, M. H. Henzinger, and V. Loitzenbauer, “Model and objective separation with conditional lower bounds: disjunction is harder than conjunction,” in <i>Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science</i>, New York, NY, USA, 2016, pp. 197–206.","ista":"Chatterjee K, Dvoák W, Henzinger MH, Loitzenbauer V. 2016. Model and objective separation with conditional lower bounds: disjunction is harder than conjunction. Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, Proceedings Symposium on Logic in Computer Science, , 197–206.","chicago":"Chatterjee, Krishnendu, Wolfgang Dvoák, Monika H Henzinger, and Veronika Loitzenbauer. “Model and Objective Separation with Conditional Lower Bounds: Disjunction Is Harder than Conjunction.” In <i>Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 197–206. IEEE, 2016. <a href=\"https://doi.org/10.1145/2933575.2935304\">https://doi.org/10.1145/2933575.2935304</a>.","apa":"Chatterjee, K., Dvoák, W., Henzinger, M. H., &#38; Loitzenbauer, V. (2016). Model and objective separation with conditional lower bounds: disjunction is harder than conjunction. In <i>Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 197–206). New York, NY, USA: IEEE. <a href=\"https://doi.org/10.1145/2933575.2935304\">https://doi.org/10.1145/2933575.2935304</a>"},"scopus_import":"1","quality_controlled":"1","title":"Model and objective separation with conditional lower bounds: disjunction is harder than conjunction","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02670"}],"oa_version":"Preprint","publist_id":"6219","language":[{"iso":"eng"}],"day":"05","year":"2016","publisher":"IEEE","date_published":"2016-07-05T00:00:00Z"}