{"publication_status":"published","day":"14","acknowledgement":"The research was partially supported by the Hong Kong Research Grants Council ECS\r\nProject No. 26208122, ERC CoG 863818 (FoRM-SMArt), the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385, HKUST– Kaisa Joint Research Institute Project Grant HKJRI3A-055 and HKUST Startup Grant R9272. Ali Ahmadi and Roodabeh Safavi were interns at HKUST.","doi":"10.4230/LIPIcs.FSTTCS.2022.29","month":"12","department":[{"_id":"KrCh"},{"_id":"GradSch"}],"file_date_updated":"2023-01-20T10:39:44Z","date_updated":"2025-04-14T07:52:56Z","article_number":"29","language":[{"iso":"eng"}],"has_accepted_license":"1","oa":1,"publication":"42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","date_created":"2023-01-01T23:00:50Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"license":"https://creativecommons.org/licenses/by/4.0/","quality_controlled":"1","author":[{"first_name":"Ali","full_name":"Ahmadi, Ali","last_name":"Ahmadi"},{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","last_name":"Chatterjee"},{"last_name":"Goharshady","orcid":"0000-0003-1702-6584","id":"391365CE-F248-11E8-B48F-1D18A9856A87","first_name":"Amir Kafshdar","full_name":"Goharshady, Amir Kafshdar"},{"full_name":"Meggendorfer, Tobias","first_name":"Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","orcid":"0000-0002-1712-2165","last_name":"Meggendorfer"},{"last_name":"Safavi Hemami","full_name":"Safavi Hemami, Roodabeh","first_name":"Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154"},{"id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","first_name":"Dorde","full_name":"Zikelic, Dorde","last_name":"Zikelic","orcid":"0000-0002-4681-1699"}],"title":"Algorithms and hardness results for computing cores of Markov chains","year":"2022","publication_identifier":{"isbn":["9783959772617"],"issn":["1868-8969"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, and a probability threshold ε, an ε-core is a subset C of states that is left with probability at most ε. More formally, C ⊆ V is an ε-core, iff ℙ[reach (V\\C)] ≤ ε. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal ε-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an ε-core of a given size is NP-complete. This solves an open problem posed in [Jan Kretínský and Tobias Meggendorfer, 2020]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal ε-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset."}],"scopus_import":"1","status":"public","ec_funded":1,"oa_version":"Published Version","conference":{"name":"FSTTCS: Foundations of Software Technology and Theoretical Computer Science","end_date":"2022-12-20","location":"Madras, India","start_date":"2022-12-18"},"date_published":"2022-12-14T00:00:00Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ddc":["000"],"article_processing_charge":"No","intvolume":"       250","volume":250,"type":"conference","corr_author":"1","_id":"12102","project":[{"grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"file":[{"date_updated":"2023-01-20T10:39:44Z","file_id":"12324","file_name":"2022_LIPICs_Ahmadi.pdf","success":1,"date_created":"2023-01-20T10:39:44Z","file_size":872534,"relation":"main_file","access_level":"open_access","checksum":"6660c802489013f034c9e8bd57f4d46e","creator":"dernst","content_type":"application/pdf"}]}