{"oa":1,"license":"https://creativecommons.org/licenses/by/4.0/","_id":"12102","title":"Algorithms and hardness results for computing cores of Markov chains","ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_created":"2023-01-01T23:00:50Z","has_accepted_license":"1","scopus_import":"1","abstract":[{"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.","lang":"eng"}],"publication":"42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","quality_controlled":"1","day":"14","file_date_updated":"2023-01-20T10:39:44Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2022-12-14T00:00:00Z","author":[{"first_name":"Ali","last_name":"Ahmadi","full_name":"Ahmadi, Ali"},{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","full_name":"Goharshady, Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-1712-2165","first_name":"Tobias","last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","full_name":"Meggendorfer, Tobias"},{"last_name":"Safavi Hemami","first_name":"Roodabeh","full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154"},{"last_name":"Zikelic","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","full_name":"Zikelic, Dorde"}],"publication_identifier":{"isbn":["9783959772617"],"issn":["1868-8969"]},"article_processing_charge":"No","language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"file":[{"date_created":"2023-01-20T10:39:44Z","file_id":"12324","success":1,"creator":"dernst","relation":"main_file","checksum":"6660c802489013f034c9e8bd57f4d46e","file_size":872534,"date_updated":"2023-01-20T10:39:44Z","file_name":"2022_LIPICs_Ahmadi.pdf","access_level":"open_access","content_type":"application/pdf"}],"article_number":"29","date_updated":"2023-02-07T09:19:43Z","volume":250,"doi":"10.4230/LIPIcs.FSTTCS.2022.29","intvolume":"       250","conference":{"end_date":"2022-12-20","location":"Madras, India","start_date":"2022-12-18","name":"FSTTC: Foundations of Software Technology and Theoretical Computer Science"},"year":"2022","type":"conference","month":"12","department":[{"_id":"KrCh"},{"_id":"GradSch"}],"citation":{"mla":"Ahmadi, Ali, et al. “Algorithms and Hardness Results for Computing Cores of Markov Chains.” <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, vol. 250, 29, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29\">10.4230/LIPIcs.FSTTCS.2022.29</a>.","apa":"Ahmadi, A., Chatterjee, K., Goharshady, A. K., Meggendorfer, T., Safavi Hemami, R., &#38; Zikelic, D. (2022). Algorithms and hardness results for computing cores of Markov chains. In <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i> (Vol. 250). Madras, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29\">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29</a>","short":"A. Ahmadi, K. Chatterjee, A.K. Goharshady, T. Meggendorfer, R. Safavi Hemami, D. Zikelic, in:, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","chicago":"Ahmadi, Ali, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, Roodabeh Safavi Hemami, and Dorde Zikelic. “Algorithms and Hardness Results for Computing Cores of Markov Chains.” In <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Vol. 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29\">https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29</a>.","ama":"Ahmadi A, Chatterjee K, Goharshady AK, Meggendorfer T, Safavi Hemami R, Zikelic D. Algorithms and hardness results for computing cores of Markov chains. In: <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29\">10.4230/LIPIcs.FSTTCS.2022.29</a>","ista":"Ahmadi A, Chatterjee K, Goharshady AK, Meggendorfer T, Safavi Hemami R, Zikelic D. 2022. Algorithms and hardness results for computing cores of Markov chains. 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTC: Foundations of Software Technology and Theoretical Computer Science vol. 250, 29.","ieee":"A. Ahmadi, K. Chatterjee, A. K. Goharshady, T. Meggendorfer, R. Safavi Hemami, and D. Zikelic, “Algorithms and hardness results for computing cores of Markov chains,” in <i>42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Madras, India, 2022, vol. 250."},"publication_status":"published","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."}