{"id":"https://openalex.org/W4310877811","doi":"https://doi.org/10.1109/tac.2022.3211959","title":"Exact Computation of Maximal Invariant Sets for Safe Markov Chains\u2014Lattice Theoretic Approach","display_name":"Exact Computation of Maximal Invariant Sets for Safe Markov Chains\u2014Lattice Theoretic Approach","publication_year":2022,"publication_date":"2022-10-04","ids":{"openalex":"https://openalex.org/W4310877811","doi":"https://doi.org/10.1109/tac.2022.3211959"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3211959","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3211959","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067147817","display_name":"Dylan Janak","orcid":"https://orcid.org/0000-0002-4047-365X"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dylan Janak","raw_affiliation_strings":["Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA"],"raw_orcid":"https://orcid.org/0000-0002-4047-365X","affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I46020346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025996200","display_name":"Pierre-Lo\u00efc Garoche","orcid":"https://orcid.org/0000-0002-0513-6076"},"institutions":[{"id":"https://openalex.org/I100296615","display_name":"\u00c9cole Nationale de l\u2019Aviation Civile","ror":"https://ror.org/022zdgq74","country_code":"FR","type":"education","lineage":["https://openalex.org/I100296615"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre-Loic Garoche","raw_affiliation_strings":["CS, ENAC, Toulouse, France"],"raw_orcid":"https://orcid.org/0000-0002-0513-6076","affiliations":[{"raw_affiliation_string":"CS, ENAC, Toulouse, France","institution_ids":["https://openalex.org/I100296615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108715154","display_name":"Behcet Ackmese","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behcet Ackmese","raw_affiliation_strings":["Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA"],"raw_orcid":"https://orcid.org/0000-0002-8693-8109","affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I46020346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1962,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.44933093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"67","issue":"12","first_page":"6980","last_page":"6986"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.7532978057861328},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6629040837287903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5937843322753906},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5087764859199524},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4740830659866333},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47367388010025024},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.47093191742897034},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37057948112487793},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37032368779182434},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3423774242401123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30191153287887573}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7532978057861328},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6629040837287903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5937843322753906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5087764859199524},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4740830659866333},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47367388010025024},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.47093191742897034},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37057948112487793},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37032368779182434},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3423774242401123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30191153287887573},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2022.3211959","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3211959","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04051117v1","is_oa":false,"landing_page_url":"https://enac.hal.science/hal-04051117","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2022, 67 (12), pp.6980-6986. ⟨10.1109/TAC.2022.3211959⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1804209111","display_name":null,"funder_award_id":"CMMI-2105502","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G5416932999","display_name":"Formal and Exhaustive Analyses of Numerical Intensive Control Software for Embedded Systems","funder_award_id":"ANR-17-CE25-0018","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W74080381","https://openalex.org/W1483568252","https://openalex.org/W1880805667","https://openalex.org/W2043100293","https://openalex.org/W2046213250","https://openalex.org/W2047360753","https://openalex.org/W2057133391","https://openalex.org/W2073976706","https://openalex.org/W2080526726","https://openalex.org/W2085683277","https://openalex.org/W2095233962","https://openalex.org/W2098530662","https://openalex.org/W2107833418","https://openalex.org/W2116403087","https://openalex.org/W2127580532","https://openalex.org/W2159089602","https://openalex.org/W2171505650","https://openalex.org/W2490159793","https://openalex.org/W2771872941","https://openalex.org/W2972554973","https://openalex.org/W4301621763"],"related_works":["https://openalex.org/W3204184292","https://openalex.org/W3176564347","https://openalex.org/W2355833770","https://openalex.org/W1985458517","https://openalex.org/W3031039437","https://openalex.org/W183202219","https://openalex.org/W3095877357","https://openalex.org/W2072565696","https://openalex.org/W2050451745","https://openalex.org/W2378903222"],"abstract_inverted_index":{"Set":[0],"theoretic":[1,18],"analysis":[2],"plays":[3],"a":[4,37,42,55,86],"crucial":[5],"part":[6],"in":[7,131],"understanding":[8],"safety":[9,32,57,73],"requirements":[10],"for":[11,64,80,85],"control":[12],"systems.":[13],"We":[14,35,75],"apply":[15],"the":[16,26,50,65,84,101,105,114,126,136],"lattice":[17],"insights":[19],"of":[20,68,83,104],"fixed":[21],"point":[22],"theorems":[23],"to":[24,93,98],"construct":[25],"maximal":[27,51,128],"invariant":[28,52,129],"set":[29,53,130],"and":[30,59,135],"verify":[31],"constraint":[33],"satisfaction.":[34],"present":[36,119],"Kleene":[38,106],"iteration-based":[39],"algorithm":[40,63,108],"with":[41],"novel":[43],"initialization\u2014based":[44],"on":[45],"omega-limit":[46],"sets\u2014for":[47],"exactly":[48],"computing":[49],"under":[54,71],"general":[56,87],"constraint,":[58],"we":[60,118],"analyze":[61],"this":[62],"special":[66],"case":[67],"Markov":[69,94],"chains":[70],"polyhedral":[72],"constraints.":[74],"also":[76],"establish":[77],"sufficient":[78],"conditions":[79],"finite":[81],"termination":[82],"discrete-time":[88],"system,":[89],"which":[90],"is":[91],"applicable":[92],"chains.":[95],"In":[96],"addition":[97],"proving":[99],"that":[100],"new":[102],"initialization":[103],"iteration":[107],"requires":[109],"no":[110],"more":[111],"iterations":[112,134],"than":[113],"previously":[115],"considered":[116],"initialization,":[117],"an":[120],"example":[121],"where":[122],"our":[123],"method":[124,138],"computes":[125],"exact":[127],"finitely":[132],"many":[133],"previous":[137],"does":[139],"not.":[140]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}