{"id":"https://openalex.org/W6948063795","doi":"https://doi.org/10.4230/lipics.sat.2025.10","title":"Fine-Grained Complexity Analysis of Dependency Quantified Boolean Formulas","display_name":"Fine-Grained Complexity Analysis of Dependency Quantified Boolean Formulas","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W6948063795","doi":"https://doi.org/10.4230/lipics.sat.2025.10"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:23744","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.10","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol341-sat2025/LIPIcs.SAT.2025.10/LIPIcs.SAT.2025.10.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol341-sat2025/LIPIcs.SAT.2025.10/LIPIcs.SAT.2025.10.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cheng, Che","orcid":"https://orcid.org/0009-0009-9126-3239"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Cheng, Che","raw_affiliation_strings":["Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan"],"raw_orcid":"https://orcid.org/0009-0009-9126-3239","affiliations":[{"raw_affiliation_string":"Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Fung, Long-Hin","orcid":"https://orcid.org/0009-0004-0972-9188"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Fung, Long-Hin","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan"],"raw_orcid":"https://orcid.org/0009-0004-0972-9188","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jiang, Jie-Hong Roland","orcid":"https://orcid.org/0000-0002-2279-4732"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jiang, Jie-Hong Roland","raw_affiliation_strings":["Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-2279-4732","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Slivovsky, Friedrich","orcid":"https://orcid.org/0000-0003-1784-2346"},"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":"Slivovsky, Friedrich","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, UK"],"raw_orcid":"https://orcid.org/0000-0003-1784-2346","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":null,"display_name":"Tan, Tony","orcid":"https://orcid.org/0009-0005-8341-2004"},"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":"Tan, Tony","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, UK"],"raw_orcid":"https://orcid.org/0009-0005-8341-2004","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43617021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.46939998865127563,"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":0.46939998865127563,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.10809999704360962,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.0925000011920929,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.7268000245094299},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.664900004863739},{"id":"https://openalex.org/keywords/disjunctive-normal-form","display_name":"Disjunctive normal form","score":0.6593000292778015},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6523000001907349},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.5831999778747559},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.5827000141143799},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.5620999932289124},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4205000102519989},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.40310001373291016}],"concepts":[{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.7268000245094299},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.664900004863739},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6523000001907349},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6523000001907349},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.5831999778747559},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.5827000141143799},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.5620999932289124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4952999949455261},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.3785000145435333},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3345000147819519},{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.33390000462532043},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3190999925136566},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.3111000061035156},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.29280000925064087},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2906000018119812},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.27619999647140503},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2583000063896179},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:23744","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.10","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol341-sat2025/LIPIcs.SAT.2025.10/LIPIcs.SAT.2025.10.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.sat.2025.10","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.sat.2025.10","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:23744","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.10","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol341-sat2025/LIPIcs.SAT.2025.10/LIPIcs.SAT.2025.10.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W6948063795.pdf","grobid_xml":"https://content.openalex.org/works/W6948063795.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Dependency":[0],"Quantified":[1,6],"Boolean":[2,7],"Formulas":[3,8],"(DQBF)":[4],"extend":[5],"by":[9],"allowing":[10],"each":[11],"existential":[12,51],"variable":[13],"to":[14,41,127],"depend":[15],"on":[16,57,81],"an":[17],"explicitly":[18],"specified":[19],"subset":[20],"of":[21,47,117],"the":[22,45,58,82,107,115],"universal":[23],"variables.":[24],"The":[25],"satisfiability":[26],"problem":[27],"for":[28,122,129],"DQBF":[29,48],"is":[30,64,94,98,109],"NEXP-complete":[31,128],"in":[32,65],"general,":[33],"with":[34,49,101,124,131],"only":[35],"a":[36,90],"few":[37],"tractable":[38],"fragments":[39],"known":[40],"date.":[42],"We":[43],"investigate":[44],"complexity":[46,116],"k":[50],"variables":[52],"(k-DQBF)":[53],"under":[54,79],"structural":[55],"restrictions":[56],"matrix":[59],"-":[60,75],"specifically,":[61],"when":[62],"it":[63],"Conjunctive":[66],"Normal":[67,72],"Form":[68,73],"(CNF)":[69],"or":[70],"Disjunctive":[71],"(DNF)":[74],"as":[76,78],"well":[77],"constraints":[80],"dependency":[83],"sets.":[84],"For":[85,104],"DNF":[86],"matrices,":[87,106],"we":[88,112],"obtain":[89],"clear":[91],"classification:":[92],"2-DQBF":[93,123],"PSPACE-complete,":[95],"while":[96],"3-DQBF":[97],"NEXP-hard,":[99],"even":[100],"disjoint":[102,125],"dependencies.":[103,133],"CNF":[105],"picture":[108],"more":[110],"nuanced:":[111],"show":[113],"that":[114],"k-DQBF":[118],"ranges":[119],"from":[120],"NL-complete":[121],"dependencies":[126],"6-DQBF":[130],"arbitrary":[132]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}