{"id":"https://openalex.org/W2056093557","doi":"https://doi.org/10.2168/lmcs-9(2:4)2013","title":"Two Variable vs. Linear Temporal Logic in Model Checking and Games","display_name":"Two Variable vs. Linear Temporal Logic in Model Checking and Games","publication_year":2013,"publication_date":"2013-05-23","ids":{"openalex":"https://openalex.org/W2056093557","doi":"https://doi.org/10.2168/lmcs-9(2:4)2013","mag":"2056093557"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-9(2:4)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(2:4)2013","pdf_url":"https://lmcs.episciences.org/1103/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/1103/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Michael Benedikt","orcid":"https://orcid.org/0000-0003-2964-0880"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michael Benedikt","raw_affiliation_strings":["Department of Computer Science, University of Oxford, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-2964-0880","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Rastislav Lenhardt","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rastislav Lenhardt","raw_affiliation_strings":["Department of Computer Science, University of Oxford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":null,"display_name":"James Worrell","orcid":"https://orcid.org/0000-0001-8151-2443"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Worrell","raw_affiliation_strings":["Department of Computer Science, University of Oxford, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0001-8151-2443","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1174,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79336226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"Volume 9, Issue 2","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9847999811172485,"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":0.9847999811172485,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.006200000178068876,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.0024999999441206455,"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/linear-temporal-logic","display_name":"Linear temporal logic","score":0.8220999836921692},{"id":"https://openalex.org/keywords/temporal-logic","display_name":"Temporal logic","score":0.7875999808311462},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.6938999891281128},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.6571999788284302},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.6528000235557556},{"id":"https://openalex.org/keywords/interval-temporal-logic","display_name":"Interval temporal logic","score":0.5480999946594238},{"id":"https://openalex.org/keywords/computation-tree-logic","display_name":"Computation tree logic","score":0.49810001254081726},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.45730000734329224},{"id":"https://openalex.org/keywords/temporal-logic-of-actions","display_name":"Temporal logic of actions","score":0.438400000333786},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3917999863624573}],"concepts":[{"id":"https://openalex.org/C4777664","wikidata":"https://www.wikidata.org/wiki/Q1536492","display_name":"Linear temporal logic","level":2,"score":0.8220999836921692},{"id":"https://openalex.org/C25016198","wikidata":"https://www.wikidata.org/wiki/Q781833","display_name":"Temporal logic","level":2,"score":0.7875999808311462},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.6938999891281128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6653000116348267},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.6571999788284302},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.6528000235557556},{"id":"https://openalex.org/C162670838","wikidata":"https://www.wikidata.org/wiki/Q6057295","display_name":"Interval temporal logic","level":3,"score":0.5480999946594238},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5242000222206116},{"id":"https://openalex.org/C198008173","wikidata":"https://www.wikidata.org/wiki/Q1040040","display_name":"Computation tree logic","level":3,"score":0.49810001254081726},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C11648818","wikidata":"https://www.wikidata.org/wiki/Q2403081","display_name":"Temporal logic of actions","level":4,"score":0.438400000333786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4372999966144562},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.3230000138282776},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.2906000018119812},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C2776493592","wikidata":"https://www.wikidata.org/wiki/Q5158717","display_name":"Succinctness","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.2752000093460083},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27219998836517334},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.26499998569488525},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C165753454","wikidata":"https://www.wikidata.org/wiki/Q1020380","display_name":"B\u00fcchi automaton","level":4,"score":0.26109999418258667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25839999318122864},{"id":"https://openalex.org/C201677973","wikidata":"https://www.wikidata.org/wiki/Q1209840","display_name":"Specification language","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.25459998846054077},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-9(2:4)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(2:4)2013","pdf_url":"https://lmcs.episciences.org/1103/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1303.4533","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.4533","pdf_url":"https://arxiv.org/pdf/1303.4533","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:afdd49808cf84af08377eabf3c45f642","is_oa":true,"landing_page_url":"https://doaj.org/article/afdd49808cf84af08377eabf3c45f642","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 9, Issue 2 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-9(2:4)2013","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-9(2:4)2013","pdf_url":"https://lmcs.episciences.org/1103/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1929273819","display_name":"Enforcement of Constraints on XML Streams","funder_award_id":"EP/G004021/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5565678245","display_name":"Model Checking Timed Systems with Restricted Resources: Algorithms and Complexity","funder_award_id":"EP/G069727/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6988580151","display_name":null,"funder_award_id":"EP/H017690/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7414769029","display_name":"Query-driven Data Acquisition from Web-based Data Sources","funder_award_id":"EP/H017690/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8438685197","display_name":null,"funder_award_id":"EP/H017690/1","funder_id":"https://openalex.org/F4320314731","funder_display_name":"UK Research and Innovation"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056093557.pdf","grobid_xml":"https://content.openalex.org/works/W2056093557.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Model":[0],"checking":[1,219],"linear-time":[2],"properties":[3,220],"expressed":[4],"in":[5],"first-order":[6,35],"logic":[7,31,36,94],"has":[8],"non-elementary":[9],"complexity,":[10],"and":[11,33,48,77,120,132,150,152,167,172,181,213,215,237,253],"thus":[12],"various":[13,78,153],"restricted":[14,26],"logical":[15],"languages":[16],"are":[17],"employed.":[18],"In":[19,87],"this":[20],"paper":[21],"we":[22,89,106,193],"consider":[23,108],"two":[24],"such":[25],"specification":[27],"logics,":[28],"linear":[29],"temporal":[30,93],"(LTL)":[32],"two-variable":[34],"(FO2).":[37],"LTL":[38,99],"is":[39,51,101],"more":[40,46],"expressive":[41],"but":[42],"FO2":[43,149,197,212,236],"can":[44,141],"be":[45,56,142],"succinct,":[47],"hence":[49],"it":[50],"not":[52],"clear":[53],"which":[54,140],"should":[55],"easier":[57],"to":[58,104,144,158,231],"verify.":[59],"We":[60,135,155,185,204],"take":[61],"a":[62,69,82,96,207,228,241],"comprehensive":[63,243],"look":[64,90,194],"at":[65,91,195],"the":[66,109,117,121,130,217,233,246],"issue,":[67],"giving":[68],"comparison":[70],"of":[71,85,98,112,125,221,235,245,248],"verification":[72,198,249],"problems":[73],"for":[74,148,162,173,202,250],"FO2,":[75,113],"LTL,":[76,214,238],"sublogics":[79],"thereof":[80],"across":[81],"wide":[83],"range":[84],"models.":[86],"particular,":[88],"unary":[92],"(UTL),":[95],"subset":[97],"that":[100,209],"expressively":[102,122],"equivalent":[103,123],"FO2;":[105],"also":[107],"stutter-free":[110],"fragment":[111,124],"obtained":[114,127],"by":[115,128],"omitting":[116,129],"successor":[118],"relation,":[119],"UTL,":[126],"next":[131],"previous":[133],"connectives.":[134],"give":[136,145,226],"three":[137],"logic-to-automata":[138],"translations":[139],"used":[143],"upper":[146],"bounds":[147,161],"UTL":[151],"sublogics.":[154,255],"apply":[156],"these":[157,187,251],"get":[159],"new":[160],"both":[163,211,222,227],"non-deterministic":[164],"systems":[165,175],"(hierarchical":[166],"recursive":[168,178],"state":[169],"machines,":[170],"games)":[171],"probabilistic":[174],"(Markov":[176],"chains,":[177,180],"Markov":[179,182],"decision":[183],"processes).":[184],"couple":[186],"with":[188,200,240],"matching":[189],"lower-bound":[190],"arguments.":[191],"Next,":[192],"combining":[196],"techniques":[199],"those":[201],"LTL.":[203],"present":[205],"here":[206],"language":[208],"subsumes":[210],"inherits":[216],"model":[218],"languages.":[223],"Our":[224],"results":[225],"unified":[229],"approach":[230],"understanding":[232],"behaviour":[234],"along":[239],"nearly":[242],"picture":[244],"complexity":[247],"logics":[252],"their":[254]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}