{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Joglekar, Manas","last_name":"Joglekar","first_name":"Manas"},{"first_name":"Nisarg","last_name":"Shah","full_name":"Shah, Nisarg"}],"external_id":{"arxiv":["1202.4175"]},"date_updated":"2023-02-23T10:55:03Z","quality_controlled":"1","doi":"10.1016/j.tcs.2015.01.050","_id":"1598","year":"2015","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1202.4175","open_access":"1"}],"volume":573,"citation":{"mla":"Chatterjee, Krishnendu, et al. “Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives.” <i>Theoretical Computer Science</i>, vol. 573, no. 3, Elsevier, 2015, pp. 71–89, doi:<a href=\"https://doi.org/10.1016/j.tcs.2015.01.050\">10.1016/j.tcs.2015.01.050</a>.","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.","short":"K. Chatterjee, M. Joglekar, N. Shah, Theoretical Computer Science 573 (2015) 71–89.","ieee":"K. Chatterjee, M. Joglekar, and N. Shah, “Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives,” <i>Theoretical Computer Science</i>, vol. 573, no. 3. Elsevier, pp. 71–89, 2015.","ama":"Chatterjee K, Joglekar M, Shah N. Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. <i>Theoretical Computer Science</i>. 2015;573(3):71-89. doi:<a href=\"https://doi.org/10.1016/j.tcs.2015.01.050\">10.1016/j.tcs.2015.01.050</a>","chicago":"Chatterjee, Krishnendu, Manas Joglekar, and Nisarg Shah. “Average Case Analysis of the Classical Algorithm for Markov Decision Processes with Büchi Objectives.” <i>Theoretical Computer Science</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.tcs.2015.01.050\">https://doi.org/10.1016/j.tcs.2015.01.050</a>.","apa":"Chatterjee, K., Joglekar, M., &#38; Shah, N. (2015). Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tcs.2015.01.050\">https://doi.org/10.1016/j.tcs.2015.01.050</a>"},"month":"03","publication":"Theoretical Computer Science","publication_status":"published","status":"public","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","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2715"}]},"title":"Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives","article_processing_charge":"No","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:52:56Z","project":[{"call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","call_identifier":"FWF"},{"call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"intvolume":"       573","issue":"3","page":"71 - 89","day":"30","publisher":"Elsevier","publist_id":"5571","type":"journal_article","abstract":[{"lang":"eng","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."}],"ec_funded":1,"oa":1,"date_published":"2015-03-30T00:00:00Z","oa_version":"Preprint","department":[{"_id":"KrCh"}]}