{"_id":"1598","department":[{"_id":"KrCh"}],"page":"71 - 89","issue":"3","scopus_import":1,"citation":{"ama":"Chatterjee K, Joglekar M, Shah N. Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. *Theoretical Computer Science*. 2015;573(3):71-89. doi:10.1016/j.tcs.2015.01.050","ista":"Chatterjee K, Joglekar M, Shah N. 2015. Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. Theoretical Computer Science. 573(3), 71–89.","ieee":"K. Chatterjee, M. Joglekar, and N. Shah, “Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives,” *Theoretical Computer Science*, vol. 573, no. 3, pp. 71–89, 2015.","apa":"Chatterjee, K., Joglekar, M., & Shah, N. (2015). Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. *Theoretical Computer Science*, *573*(3), 71–89. https://doi.org/10.1016/j.tcs.2015.01.050","mla":"Chatterjee, Krishnendu, et al. “Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives.” *Theoretical Computer Science*, vol. 573, no. 3, Elsevier, 2015, pp. 71–89, doi:10.1016/j.tcs.2015.01.050.","chicago":"Chatterjee, Krishnendu, Manas Joglekar, and Nisarg Shah. “Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives.” *Theoretical Computer Science* 573, no. 3 (2015): 71–89. https://doi.org/10.1016/j.tcs.2015.01.050.","short":"K. Chatterjee, M. Joglekar, N. Shah, Theoretical Computer Science 573 (2015) 71–89."},"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1202.4175"}],"month":"03","type":"journal_article","date_created":"2018-12-11T11:52:56Z","doi":"10.1016/j.tcs.2015.01.050","ec_funded":1,"date_published":"2015-03-30T00:00:00Z","year":"2015","title":"Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives","author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Joglekar","first_name":"Manas","full_name":"Joglekar, Manas"},{"first_name":"Nisarg","full_name":"Shah, Nisarg","last_name":"Shah"}],"language":[{"iso":"eng"}],"acknowledgement":"The research was supported by FWF Grant No. P 23499-N23, FWF NFN Grant No. S11407-N23 (RiSE), ERC Start Grant (279307: Graph Games), and the Microsoft Faculty Fellows Award. Nisarg Shah is also supported by NSF Grant CCF-1215883.\r\n","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","oa":1,"volume":573,"day":"30","publication_status":"published","publisher":"Elsevier","publication":"Theoretical Computer Science","external_id":{"arxiv":["1202.4175"]},"intvolume":" 573","article_processing_charge":"No","date_updated":"2020-08-11T10:09:48Z","related_material":{"record":[{"status":"public","id":"2715","relation":"earlier_version"}]},"abstract":[{"text":"We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives, and examine the problem of computing the set of almost-sure winning vertices such that the objective can be ensured with probability 1 from these vertices. We study for the first time the average-case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average-case running time is linear (as compared to the worst-case linear number of iterations and quadratic time complexity). Second, for the average-case analysis over all MDPs we show that the expected number of iterations is constant and the average-case running time is linear (again as compared to the worst-case linear number of iterations and quadratic time complexity). Finally we also show that when all MDPs are equally likely, the probability that the classical algorithm requires more than a constant number of iterations is exponentially small.","lang":"eng"}],"quality_controlled":"1","project":[{"grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407","name":"Game Theory"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"publist_id":"5571"}