{"id":"https://openalex.org/W4406246652","doi":"https://doi.org/10.46298/lmcs-21(1:3)2025","title":"HyperLTL Satisfiability Is Highly Undecidable, HyperCTL$^*$ is Even Harder","display_name":"HyperLTL Satisfiability Is Highly Undecidable, HyperCTL$^*$ is Even Harder","publication_year":2025,"publication_date":"2025-01-10","ids":{"openalex":"https://openalex.org/W4406246652","doi":"https://doi.org/10.46298/lmcs-21(1:3)2025"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-21(1:3)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:3)2025","pdf_url":"https://lmcs.episciences.org/15048/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/15048/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002354883","display_name":"Marie Fortin","orcid":"https://orcid.org/0000-0002-7045-4783"},"institutions":[{"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"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marie Fortin","raw_affiliation_strings":["IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","CNRS - Centre National de la Recherche Scientifique (France)"],"affiliations":[{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","institution_ids":["https://openalex.org/I4210091437","https://openalex.org/I204730241"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091303743","display_name":"Louwe B. Kuijer","orcid":"https://orcid.org/0000-0001-6696-9023"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Louwe B. Kuijer","raw_affiliation_strings":["University of Liverpool (Liverpool L69 3BX, United Kingdom - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"University of Liverpool (Liverpool L69 3BX, United Kingdom - United Kingdom)","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060577776","display_name":"Patrick Totzke","orcid":"https://orcid.org/0000-0001-5274-8190"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Patrick Totzke","raw_affiliation_strings":["University of Liverpool (Liverpool L69 3BX, United Kingdom - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"University of Liverpool (Liverpool L69 3BX, United Kingdom - United Kingdom)","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064596121","display_name":"Mart\u00edn Zimmermann","orcid":"https://orcid.org/0000-0002-8038-2453"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Martin Zimmermann","raw_affiliation_strings":["AAU - Aalborg University [Denmark] (Fredrik Bajers Vej 5, P.O. Box 159, DK - 9100 Aalborg, Denmark - Denmark)"],"affiliations":[{"raw_affiliation_string":"AAU - Aalborg University [Denmark] (Fredrik Bajers Vej 5, P.O. Box 159, DK - 9100 Aalborg, Denmark - Denmark)","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002354883"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210117673"],"apc_list":null,"apc_paid":null,"fwci":4.1237,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92834923,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"Volume 21, Issue 1","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":0.996999979019165,"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":0.996999979019165,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9900000095367432,"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/T11424","display_name":"Security and Verification in Computing","score":0.9898999929428101,"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/undecidable-problem","display_name":"Undecidable problem","score":0.9559990763664246},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.7107606530189514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6694760322570801},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.512481689453125},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36441636085510254},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.3341454267501831},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.32530829310417175}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9559990763664246},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.7107606530189514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6694760322570801},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.512481689453125},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36441636085510254},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.3341454267501831},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.32530829310417175}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.46298/lmcs-21(1:3)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:3)2025","pdf_url":"https://lmcs.episciences.org/15048/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:pure.atira.dk:openaire/1394de33-6f7b-44fe-9da2-400c70f7af7d","is_oa":true,"landing_page_url":"https://vbn.aau.dk/da/publications/1394de33-6f7b-44fe-9da2-400c70f7af7d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fortin, M, Kuijer, L B, Totzke, P & Zimmermann, M 2025, 'HyperLTL Satisfiability Is Highly Undecidable, HyperCTL\u2217 is Even Harder', Logical Methods in Computer Science, vol. 21, no. 1, pp. 3:1-3:39. https://doi.org/10.46298/lmcs-21(1:3)2025","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-05354525v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05354525","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, 2025, Volume 21, Issue 1, &#x27E8;10.46298/lmcs-21(1:3)2025&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:570acda7f1d74c53831fc051b5c0a7cf","is_oa":true,"landing_page_url":"https://doaj.org/article/570acda7f1d74c53831fc051b5c0a7cf","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 21, Issue 1 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-21(1:3)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:3)2025","pdf_url":"https://lmcs.episciences.org/15048/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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G1928332608","display_name":"COSTRA -- The Cost of Winning Strategies","funder_award_id":"EP/V025848/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4497834054","display_name":null,"funder_award_id":"EP/X042596/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5009292347","display_name":null,"funder_award_id":"EP/V025848/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8624711644","display_name":"quantMD: Ontology-Based Management of Many-Dimensional Quantitative Data","funder_award_id":"EP/S032207/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8841539657","display_name":null,"funder_award_id":"EP/S032207/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406246652.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1213177963","https://openalex.org/W1501571921","https://openalex.org/W1970999740","https://openalex.org/W2004306067","https://openalex.org/W2013085432","https://openalex.org/W2023808162","https://openalex.org/W2039934838","https://openalex.org/W2106878575","https://openalex.org/W2117832390","https://openalex.org/W2342178224","https://openalex.org/W2517913729","https://openalex.org/W2523320959","https://openalex.org/W2529025013","https://openalex.org/W2539229089","https://openalex.org/W2603022255","https://openalex.org/W2734723004","https://openalex.org/W2801746908","https://openalex.org/W2885490371","https://openalex.org/W2894415726","https://openalex.org/W2961595086","https://openalex.org/W2963563466","https://openalex.org/W2963829406","https://openalex.org/W2964335063","https://openalex.org/W2994155569","https://openalex.org/W3003336482","https://openalex.org/W3021212273","https://openalex.org/W3042541527","https://openalex.org/W3047023789","https://openalex.org/W3097045895","https://openalex.org/W3097615709","https://openalex.org/W3117377366","https://openalex.org/W3118247109","https://openalex.org/W3165398732","https://openalex.org/W3177160037","https://openalex.org/W3184417962","https://openalex.org/W3201171525","https://openalex.org/W3206405735","https://openalex.org/W4230702118","https://openalex.org/W4250728693","https://openalex.org/W4281769808","https://openalex.org/W4285269273","https://openalex.org/W4289745775","https://openalex.org/W4290087444","https://openalex.org/W4366722387","https://openalex.org/W4366725162","https://openalex.org/W4378901237","https://openalex.org/W4384573104","https://openalex.org/W4393261799","https://openalex.org/W4396820466","https://openalex.org/W4403799162","https://openalex.org/W4405255264","https://openalex.org/W4412211691"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W2989332944","https://openalex.org/W2021891065","https://openalex.org/W2583549044","https://openalex.org/W2119045600","https://openalex.org/W2584984136","https://openalex.org/W2170336571","https://openalex.org/W2962928105","https://openalex.org/W2585890227","https://openalex.org/W1543051890"],"abstract_inverted_index":{"Temporal":[0],"logics":[1,24],"for":[2,51,103,145,166],"the":[3,59,90,96,119,121,163,170],"specification":[4],"of":[5,16,62,125,169],"information-flow":[6],"properties":[7],"are":[8,25,68,86,147],"able":[9],"to":[10,118,133],"express":[11],"relations":[12],"between":[13],"multiple":[14],"executions":[15],"a":[17,45,113],"system.":[18],"The":[19],"two":[20],"most":[21],"important":[22],"such":[23],"HyperLTL":[26,76,171],"and":[27,32,80,95,142],"HyperCTL*,":[28,104],"which":[29],"generalise":[30],"LTL":[31],"CTL*":[33],"by":[34],"trace":[35],"quantification.":[36],"It":[37],"is":[38,49,78,83,116,175],"known":[39,92],"that":[40,66,75,107,115,139,162],"this":[41,55,126,131],"expressiveness":[42],"comes":[43],"at":[44],"price,":[46],"i.e.":[47,155],"satisfiability":[48,77,82,144],"undecidable":[50],"both":[52,67,140],"logics.":[53],"In":[54],"paper":[56],"we":[57,73,105,137,160],"settle":[58],"exact":[60],"complexity":[61],"these":[63],"problems,":[64],"showing":[65],"in":[69,152],"fact":[70],"highly":[71,157],"undecidable:":[72],"prove":[74,101,106,130,138],"$\\Sigma_1^1$-complete":[79],"HyperCTL*":[81,110,146],"$\\Sigma_1^2$-complete.":[84],"These":[85],"significant":[87],"increases":[88],"over":[89],"previously":[91],"lower":[93],"bounds":[94],"first":[97,122],"upper":[98,123],"bounds.":[99],"To":[100],"$\\Sigma_1^2$-membership":[102],"every":[108,167],"satisfiable":[109],"sentence":[111],"has":[112],"model":[114],"equinumerous":[117],"continuum,":[120],"bound":[124,132],"kind.":[127],"We":[128],"also":[129],"be":[134],"tight.":[135],"Furthermore,":[136],"countable":[141],"finitely-branching":[143],"as":[148,150],"hard":[149],"truth":[151],"second-order":[153],"arithmetic,":[154],"still":[156],"undecidable.":[158],"Finally,":[159],"show":[161],"membership":[164],"problem":[165],"level":[168],"quantifier":[172],"alternation":[173],"hierarchy":[174],"$\\Pi_1^1$-complete.":[176],"Comment:":[177],"arXiv":[178],"admin":[179],"note:":[180],"substantial":[181],"text":[182],"overlap":[183],"with":[184],"arXiv:2105.04176":[185]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
