{"type":"ScholarlyArticle","title":"The Complexity of Model Checking Knowledge and Time","authors":[{"name":"Laura Bozzelli","slug":"laura-bozzelli","given":"Laura","family":"Bozzelli","affiliation":"Università degli Studi di Napoli \"Federico II\" , Italy"},{"name":"Bastien Maubert","slug":"bastien-maubert","given":"Bastien","family":"Maubert","affiliation":"Università degli Studi di Napoli \"Federico II\" , Italy"},{"name":"Aniello Murano","slug":"aniello-murano","given":"Aniello","family":"Murano","affiliation":"Università degli Studi di Napoli \"Federico II\" , Italy"}],"abstract":"We establish the precise complexity of the model checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL* with knowledge, and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL.","doi":"10.24963/ijcai.2019/221","url":"https://ijcai.org/proceedings/2019/221","pdf":"https://ijcai.org/proceedings/2019/0221.pdf","markdown":"https://ijcai.org/proceedings/2019/221.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/221","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":221,"pages":{"first":1595,"last":1601},"keywords":["Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis","Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief","Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Non-classical Logics for Knowledge Representation"],"videos":[],"references":[{"position":1,"raw":"[Alur et al., 2007] Rajeev Alur, Pavol Černỳ, and Swarat Chaudhuri. Model checking on trees with path equiva- lences. In TACAS, pages 664-678. Springer, 2007.","title":"Model checking on trees with path equivalences","authors":"Rajeev Alur, Pavol Černỳ, Swarat Chaudhuri","year":"2007","venue":"TACAS","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aucher, 2014] Guillaume Aucher. Supervisory control the- ory in epistemic temporal logic. In AAMAS, pages 333- 340, 2014.","title":"Supervisory control theory in epistemic temporal logic","authors":"Guillaume Aucher, Aucher","year":"2014","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Boas, 1997] P. Van Emde Boas. The Convenience of Tilings. In Complexity, Logic, and Recursion Theory, pages 331-363.","title":"The Convenience of Tilings","authors":"P Van Emde, Boas","year":null,"venue":"Complexity, Logic, and Recursion Theory","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bozzelli et al., 2015] Laura Bozzelli, Bastien Maubert, and Sophie Pinchinat. Uniform strategies, rational relations and jumping automata. Inf. Comput., 242:80-107, 2015.","title":"Uniform strategies, rational relations and jumping automata","authors":"Laura Bozzelli, Bastien Maubert, Sophie Pinchinat","year":"2015","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Dechesne and Wang, 2010] Francien Dechesne and Yanjing Wang. To know or not to know: epistemic approaches to security protocol verification. Synthese, 177(1):51-76, 2010.","title":"Francien Dechesne and Yanjing Wang. To know or not to know: epistemic approaches to security protocol verification","authors":"Wang Dechesne","year":"2010","venue":"Synthese","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dima, 2009] Cȃtȃlin Dima. Revisiting satisfiability and model-checking for ctlk with synchrony and perfect recall. In CLIMA, pages 117-131, 2009.","title":"Cȃtȃlin Dima. Revisiting satisfiability and model-checking for ctlk with synchrony and perfect recall","authors":"Dima","year":"2009","venue":"CLIMA","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Emerson and Halpern, 1986] E. Allen Emerson and Joseph Y. Halpern. \"Sometimes\" and \"not never\" revis- ited: on branching versus linear time temporal logic. J. ACM, 33(1):151-178, 1986.","title":"Sometimes\" and \"not never\" revisited: on branching versus linear time temporal logic","authors":"E, Allen Emerson, Joseph Y Halpern","year":"1986","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Emerson and Lei, 1987] E Allen Emerson and Chin-Laung Lei. Modalities for model checking: Branching time logic strikes back. Sci. Comput. Program., 8(3):275-306, 1987.","title":"Modalities for model checking: Branching time logic strikes back","authors":"Emerson, Lei ;, Allen Emerson, Chin-Laung Lei","year":"1987","venue":"Sci. Comput. Program","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Engelhardt et al., 2007] Kai Engelhardt, Peter Gammie, and Ron Van Der Meyden. Model checking knowledge and linear time: PSPACE cases. In LFCS, pages 195-211. Springer, 2007.","title":"Model checking knowledge and linear time: PSPACE cases","authors":"Kai Engelhardt, Peter Gammie, Ron Van Der Meyden","year":"2007","venue":"LFCS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fagin et al., 2004] Ronald Fagin, Joseph Y Halpern, Yoram Moses, and Moshe Vardi. Reasoning about knowledge. MIT press, 2004.","title":"Reasoning about knowledge","authors":"Ronald Fagin, Yoram Joseph Y Halpern, Moshe Moses, Vardi","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Halpern and O'Neill, 2005] Joseph Y. Halpern and Kevin R. O'Neill. Anonymity and information hiding in multiagent systems. J. Comput. Secur., 13(3):483-512, 2005.","title":"Anonymity and information hiding in multiagent systems","authors":"Joseph Y Halpern, Kevin R O'neill","year":"2005","venue":"J. Comput. Secur","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Halpern and Vardi, 1986] Joseph Y Halpern and Moshe Y Vardi. The complexity of reasoning about knowledge and time. In STOC, pages 304-315. ACM, 1986.","title":"The complexity of reasoning about knowledge and time","authors":"Y Joseph, Moshe Y Halpern, Vardi","year":"1986","venue":"STOC","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Halpern and Vardi, 1989] Joseph Y. Halpern and Moshe Y. Vardi. The complexity of reasoning about knowledge and time. 1. Lower bounds. J Comput. Syst. Sci., 38(1):195- 237, 1989.","title":"The complexity of reasoning about knowledge and time. 1. Lower bounds","authors":"Joseph Y Halpern, Moshe Y Vardi","year":"1989","venue":"J Comput. Syst. Sci","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Halpern et al., 2004] Joseph Y. Halpern, Ron van der Mey- den, and Moshe Y. Vardi. Complete axiomatizations for reasoning about knowledge and time. SIAM J. Comput., 33(3):674-703, 2004.","title":"Complete axiomatizations for reasoning about knowledge and time","authors":"Joseph Y Halpern, Ron Van Der Meyden, Moshe Y Vardi","year":"2004","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Huang and van der Meyden, 2010] Xiaowei Huang and Ron van der Meyden. The complexity of epistemic model checking: Clock semantics and branching time. In ECAI, pages 549-554, 2010.","title":"The complexity of epistemic model checking: Clock semantics and branching time","authors":"Van Huang, Xiaowei Der Meyden, Ron Huang, Van Der Meyden","year":"2010","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Huang et al., 2015] Xiaowei Huang, Qingliang Chen, and Kaile Su. The complexity of model checking succinct mul- tiagent systems. In IJCAI, pages 1076-1082, 2015.","title":"The complexity of model checking succinct multiagent systems","authors":"Xiaowei Huang, Qingliang Chen, Kaile Su","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kong and Lomuscio, 2017] Jeremy Kong and Alessio Lo- muscio. Symbolic model checking multi-agent systems against CTL*K specifications. In AAMAS, pages 114-122, 2017.","title":"Symbolic model checking multi-agent systems against CTL*K specifications","authors":"Lomuscio ; Alessio Kong, Lomuscio","year":"2017","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Ladner and Reif, 1986] Richard E. Ladner and John H. Reif. The logic of distributed protocols. In TARK, pages 207-222, 1986.","title":"The logic of distributed protocols","authors":"Richard E Ladner, John H Reif","year":"1986","venue":"TARK","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lomuscio and Raimondi, 2006] Alessio Lomuscio and Franco Raimondi. The complexity of model checking concurrent programs against CTLK specifications. In AAMAS, pages 548-550, 2006.","title":"The complexity of model checking concurrent programs against CTLK specifications","authors":"Alessio Lomuscio, Franco Raimondi","year":"2006","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Parikh and Ramanujam, 1985] Rohit Parikh and Ra- maswamy Ramanujam. Distributed processes and the logic of knowledge. In Logic of Programs, pages 256-268, 1985.","title":"Rohit Parikh and Ramaswamy Ramanujam. Distributed processes and the logic of knowledge","authors":"Ramanujam Parikh","year":"1985","venue":"Logic of Programs","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Pnueli, 1977] Amir Pnueli. The temporal logic of programs. In FOCS, pages 46-57. IEEE, 1977.","title":"The temporal logic of programs","authors":"Amir Pnueli, Pnueli","year":"1977","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Puchala, 2010] Bernd Puchala. Asynchronous omega- regular games with partial information. In MFCS, pages 592-603, 2010.","title":"Asynchronous omegaregular games with partial information","authors":"Bernd Puchala","year":"2010","venue":"MFCS","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Raimondi, 2006] Franco Raimondi. Model checking multi- agent systems. PhD thesis, University of London, 2006.","title":"Model checking multiagent systems","authors":"Franco Raimondi","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Reif, 1984] John H. Reif. The complexity of two-player games of incomplete information. J. Comput. Syst. Sci., 29(2):274-301, 1984.","title":"The complexity of two-player games of incomplete information","authors":"John H Reif","year":"1984","venue":"J. Comput. Syst. Sci","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[van der Meyden and Shilov, 1999] Ron van der Meyden and Nikolay V. Shilov. Model checking knowledge and time in systems with perfect recall (extended abstract). In FSTTCS, pages 432-445, 1999.","title":"Ron van der Meyden and Nikolay V. Shilov. Model checking knowledge and time in systems with perfect recall","authors":"Shilov Van Der Meyden","year":"1999","venue":"FSTTCS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[van der Meyden and Su, 2004] Ron van der Meyden and Kaile Su. Symbolic model checking the knowledge of the dining cryptographers. In CSFW, pages 280-291, 2004.","title":"Symbolic model checking the knowledge of the dining cryptographers","authors":"Su ; Van Der Meyden, Ron Van Der Meyden, Kaile Su","year":"2004","venue":"CSFW","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[van der Meyden and Vardi, 1998] Ron van der Meyden and Moshe Y Vardi. Synthesis from knowledge-based specifi- cations. In CONCUR, pages 34-49. Springer, 1998.","title":"Synthesis from knowledge-based specifications","authors":"Van Der Meyden, Moshe Y Vardi ; Ron Van Der Meyden, Vardi","year":"1998","venue":"CONCUR","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[van der Meyden, 1998] Ron van der Meyden. Common knowledge and update in finite environments. Inf. Com- put., 140(2):115-157, 1998.","title":"Ron van der Meyden. Common knowledge and update in finite environments","authors":"Van Der Meyden","year":"1998","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Vardi and Wolper, 1994] Moshe Y Vardi and Pierre Wolper. Reasoning about infinite computations. Inf. Comp., 115(1):1-37, 1994.","title":"Reasoning about infinite computations","authors":"Wolper Vardi, Moshe Y Vardi, Pierre Wolper","year":"1994","venue":"Inf. Comp","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}