{"id":"https://openalex.org/W2021112905","doi":"https://doi.org/10.1145/2629417","title":"Approximate Verification of the Symbolic Dynamics of Markov Chains","display_name":"Approximate Verification of the Symbolic Dynamics of Markov Chains","publication_year":2015,"publication_date":"2015-03-02","ids":{"openalex":"https://openalex.org/W2021112905","doi":"https://doi.org/10.1145/2629417","mag":"2021112905"},"language":"en","primary_location":{"id":"doi:10.1145/2629417","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629417","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-00920793/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104682589","display_name":"Manindra Agrawal","orcid":null},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Manindra Agrawal","raw_affiliation_strings":["Indian Institute of Technology Kanpur, India","Indian Institute of Technology , Kanpur , India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Kanpur, India","institution_ids":["https://openalex.org/I94234084"]},{"raw_affiliation_string":"Indian Institute of Technology , Kanpur , India","institution_ids":["https://openalex.org/I94234084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063753055","display_name":"S. Akshay","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Akshay","raw_affiliation_strings":["Indian Institute of Technology Bombay, India","Indian Institute of Technology, Bombay, India;"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Bombay, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology, Bombay, India;","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064810861","display_name":"Blaise Genest","orcid":"https://orcid.org/0000-0002-5758-1876"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Blaise Genest","raw_affiliation_strings":["CNRS, UMR IRISA, Rennes, France","CNRS, UMR IRISA, Rennes, France#TAB#"],"affiliations":[{"raw_affiliation_string":"CNRS, UMR IRISA, Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, UMR IRISA, Rennes, France#TAB#","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111462984","display_name":"P. S. Thiagarajan","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"P. S. Thiagarajan","raw_affiliation_strings":["National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5104682589"],"corresponding_institution_ids":["https://openalex.org/I94234084"],"apc_list":null,"apc_paid":null,"fwci":1.4554,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.83029523,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"1","first_page":"1","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9990000128746033,"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/T12029","display_name":"DNA and Biological Computing","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.6585877537727356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5883399844169617},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4895351827144623},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48623529076576233},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.45985183119773865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42094266414642334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3928230404853821},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2817683219909668},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11245894432067871},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10493576526641846}],"concepts":[{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.6585877537727356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5883399844169617},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4895351827144623},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48623529076576233},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.45985183119773865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42094266414642334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3928230404853821},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2817683219909668},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11245894432067871},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10493576526641846},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/2629417","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629417","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00920793v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00920793","pdf_url":"https://inria.hal.science/hal-00920793/document","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the ACM (JACM), 2015, 62 (1), pp.34-65. ⟨10.1145/2629417⟩","raw_type":"Journal articles"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/18305","is_oa":false,"landing_page_url":"http://doi.org/10.1145/2629417","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dspace.library.iitb.ac.in:100/18305","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/jspui/handle/100/18305","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00920793v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00920793","pdf_url":"https://inria.hal.science/hal-00920793/document","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the ACM (JACM), 2015, 62 (1), pp.34-65. ⟨10.1145/2629417⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2330135216","display_name":null,"funder_award_id":"ANR-13-BS02-0011","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2963670993","display_name":null,"funder_award_id":"IFA12","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4839418718","display_name":null,"funder_award_id":"ANR-13-BS02-0011-01, ANR-2010-BLAN-0317","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5305903771","display_name":null,"funder_award_id":"MOE2011-T2-2-012","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G5570752017","display_name":null,"funder_award_id":"IFA12-MA-17","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G6625366829","display_name":null,"funder_award_id":"DST-INSPIRE","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G7578288818","display_name":null,"funder_award_id":"ANR-2010-BLAN-0317","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8446343607","display_name":null,"funder_award_id":"ANR-13-BS02-0011-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021112905.pdf","grobid_xml":"https://content.openalex.org/works/W2021112905.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W12758337","https://openalex.org/W125598877","https://openalex.org/W125973810","https://openalex.org/W755194005","https://openalex.org/W1479674952","https://openalex.org/W1479679270","https://openalex.org/W1486013485","https://openalex.org/W1496256885","https://openalex.org/W1497670448","https://openalex.org/W1498432697","https://openalex.org/W1505443661","https://openalex.org/W1537517911","https://openalex.org/W1553142094","https://openalex.org/W1565611252","https://openalex.org/W1585038871","https://openalex.org/W1591783602","https://openalex.org/W1594530072","https://openalex.org/W1806449990","https://openalex.org/W1809182522","https://openalex.org/W1822323017","https://openalex.org/W1862398452","https://openalex.org/W1995713768","https://openalex.org/W2005998857","https://openalex.org/W2015678302","https://openalex.org/W2025406549","https://openalex.org/W2035537281","https://openalex.org/W2051638203","https://openalex.org/W2052596766","https://openalex.org/W2075087125","https://openalex.org/W2081076340","https://openalex.org/W2083494715","https://openalex.org/W2088366690","https://openalex.org/W2101508170","https://openalex.org/W2125500714","https://openalex.org/W2135706240","https://openalex.org/W2137369624","https://openalex.org/W2138856440","https://openalex.org/W2141289380","https://openalex.org/W2147340401","https://openalex.org/W2151642860","https://openalex.org/W2160999213","https://openalex.org/W2323009482","https://openalex.org/W2561675875","https://openalex.org/W2970618185","https://openalex.org/W3175367423","https://openalex.org/W4206252072","https://openalex.org/W4242358482","https://openalex.org/W4389011534"],"related_works":["https://openalex.org/W1660242800","https://openalex.org/W2141075946","https://openalex.org/W1983767262","https://openalex.org/W1967096152","https://openalex.org/W2323914380","https://openalex.org/W3102517575","https://openalex.org/W3013412531","https://openalex.org/W2947386998","https://openalex.org/W2891602308","https://openalex.org/W2142539551"],"abstract_inverted_index":{"A":[0,114],"finite-state":[1],"Markov":[2,308,407],"chain":[3,309],"M":[4,27,66,128,178,201,310],"can":[5,266,358],"be":[6,151],"regarded":[7],"as":[8,67,133,229],"a":[9,37,43,50,85,97,136,167,192,206,226,230,249],"linear":[10],"transform":[11],"operating":[12],"on":[13,300],"the":[14,63,91,120,144,152,171,197,213,245,253,289,294,301,307,313,321,349,377,392],"set":[15,44,51,71,99,122,161,193],"of":[16,26,39,45,52,65,72,100,127,138,148,162,177,194,200,205,208,248,296,306,320,373],"probability":[17,31,40,92,116,247],"distributions":[18,47,164],"over":[19,119,188,212],"its":[20,332,374,389],"node":[21,121,250],"set.":[22],"The":[23,74,160],"iterative":[24],"applications":[25,176],"to":[28,61,79,179,221,268,403],"an":[29,56,180,185,239,262,297,318,343],"initial":[30,46,181,195],"distribution":[32,117],"\u03bc":[33,118],"0":[34],"will":[35,48,150,183,202,242],"generate":[36],"trajectory":[38,315,323],"distributions.":[41],"Thus,":[42],"induce":[49,184],"trajectories.":[53,73],"It":[54],"is":[55,78,129,166,220,261,287,317],"interesting":[57],"and":[58,303,335,339],"useful":[59],"task":[60,83],"analyze":[62],"dynamics":[64,199],"defined":[68],"by":[69,174],"this":[70,82,189,286],"novel":[75],"idea":[76],"here":[77],"carry":[80],"out":[81],"in":[84,154,252,284,367,385,399],"symbolic":[86,198,314,322],"framework.":[87],"Specifically,":[88],"we":[89,281,292],"discretize":[90],"value":[93],"space":[94],"[0,1]":[95],"into":[96],"finite":[98,168,405],"intervals":[101,139],"I":[102,105,108,111,142,255,257],"=":[103],"{":[104],"1":[106],",":[107,135,369,387],"2":[109],",...,":[110],"m":[112],"}.":[113],"concrete":[115],"{1,":[123],"2,...,":[124],"n":[125],"}":[126],"then":[130,203],"symbolically":[131],"represented":[132],"D":[134,149,165,215],"tuple":[137],"drawn":[140],"from":[141,256],"where":[143],"i":[145,157],"th":[146],"component":[147],"interval":[153,254],"which":[155],"\u03bc(":[156],")":[158],"falls.":[159],"discretized":[163],"alphabet.":[169,190],"Hence,":[170],"trajectory,":[172],"generated":[173],"repeated":[175],"distribution,":[182],"infinite":[186,209,365,383],"string":[187],"Given":[191],"distributions,":[196],"consist":[204],"language":[207],"strings":[210],"L":[211,224,260,274,368,386],"alphabet":[214],".":[216,258,311],"Our":[217,352],"main":[218,353],"goal":[219],"verify":[222],"whether":[223,361],"meets":[225],"specification":[227],"given":[228,378],"linear-time":[231],"temporal":[232],"logic":[233],"formula":[234],"\u03c6.":[235],"In":[236],"our":[237,270],"logic,":[238],"atomic":[240],"proposition":[241],"assert":[243],"that":[244,356,400],"current":[246],"falls":[251],"If":[259],"\u03c9-regular":[263],"language,":[264],"one":[265,357,372],"hope":[267],"solve":[269],"model-checking":[271],"problem":[272],"(whether":[273],"\u22a7":[275],"\u03c6?)":[276],"using":[277],"standard":[278],"techniques.":[279],"However,":[280],"show":[282],"that,":[283],"general,":[285],"not":[288],"case.":[290],"Consequently,":[291],"develop":[293],"notion":[295],"\u03f5-approximation,":[298],"based":[299],"transient":[302,333,350],"long-term":[304],"behaviors":[305],"Briefly,":[312],"\u03be'":[316,327,340],"\u03f5-approximation":[319],"\u03be":[324,330,338],"iff":[325],"(1)":[326],"agrees":[328],"with":[329],"during":[331],"phase;":[334],"(2)":[336],"both":[337],"are":[341,355,397],"within":[342],"\u03f5-neighborhood":[344],"at":[345,370],"all":[346,388,404],"times":[347],"after":[348],"phase.":[351],"results":[354,396],"effectively":[359],"check":[360],"(i)":[362],"for":[363,381],"each":[364,382],"word":[366,384],"least":[371],"\u03f5-approximations":[375,390],"satisfies":[376],"specification;":[379],"(ii)":[380],"satisfy":[391],"specification.":[393],"These":[394],"verification":[395],"strong":[398],"they":[401],"apply":[402],"state":[406],"chains.":[408]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}