{"id":"https://openalex.org/W2552825470","doi":"https://doi.org/10.1145/2996796","title":"Complexity of Two-Variable Logic on Finite Trees","display_name":"Complexity of Two-Variable Logic on Finite Trees","publication_year":2016,"publication_date":"2016-11-11","ids":{"openalex":"https://openalex.org/W2552825470","doi":"https://doi.org/10.1145/2996796","mag":"2552825470"},"language":"en","primary_location":{"id":"doi:10.1145/2996796","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2996796","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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":"ACM Transactions on Computational Logic","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/A5039613878","display_name":"Saguy Benaim","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":"Saguy Benaim","raw_affiliation_strings":["University of Oxford, Parks Road, Oxford UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Parks Road, Oxford UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037774973","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":["University of Oxford, Parks Road, Oxford UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Parks Road, Oxford UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068443996","display_name":"Witold Charatonik","orcid":"https://orcid.org/0000-0001-7062-0385"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Witold Charatonik","raw_affiliation_strings":["University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090488658","display_name":"Emanuel Kiero\u0144ski","orcid":"https://orcid.org/0000-0002-8538-8221"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Emanuel Kiero\u0144ski","raw_affiliation_strings":["University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051899958","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":["University of Oxford"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004165473","display_name":"Filip Mazowiecki","orcid":"https://orcid.org/0000-0002-4535-6508"},"institutions":[{"id":"https://openalex.org/I73417466","display_name":"Coventry University","ror":"https://ror.org/01tgmhj36","country_code":"GB","type":"education","lineage":["https://openalex.org/I73417466"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Filip Mazowiecki","raw_affiliation_strings":["University of Warsaw, Coventry, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw, Coventry, UK","institution_ids":["https://openalex.org/I73417466"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068165188","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":["University of Oxford, Parks Road, Oxford UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Parks Road, Oxford UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1817,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82777496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"4","first_page":"1","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10317","display_name":"Advanced Database Systems and Queries","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10317","display_name":"Advanced Database Systems and Queries","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9991999864578247,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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/xpath","display_name":"XPath","score":0.784145712852478},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.7376217246055603},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.731302797794342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5994970202445984},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.493670791387558},{"id":"https://openalex.org/keywords/exptime","display_name":"EXPTIME","score":0.47770145535469055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4760955572128296},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.3718133270740509},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3551139831542969},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.33929380774497986},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3274343013763428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30968940258026123},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2854684591293335},{"id":"https://openalex.org/keywords/xml","display_name":"XML","score":0.1499527096748352}],"concepts":[{"id":"https://openalex.org/C2780213375","wikidata":"https://www.wikidata.org/wiki/Q16340","display_name":"XPath","level":4,"score":0.784145712852478},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.7376217246055603},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.731302797794342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5994970202445984},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.493670791387558},{"id":"https://openalex.org/C56049555","wikidata":"https://www.wikidata.org/wiki/Q1276570","display_name":"EXPTIME","level":4,"score":0.47770145535469055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4760955572128296},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.3718133270740509},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3551139831542969},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.33929380774497986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3274343013763428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30968940258026123},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2854684591293335},{"id":"https://openalex.org/C8797682","wikidata":"https://www.wikidata.org/wiki/Q2115","display_name":"XML","level":2,"score":0.1499527096748352},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55348073","wikidata":"https://www.wikidata.org/wiki/Q595926","display_name":"XML validation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2996796","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2996796","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"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":"ACM Transactions on Computational Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G4266278604","display_name":null,"funder_award_id":"EP/M012298/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4588342371","display_name":null,"funder_award_id":"DEC-2011/03/B/ST6/00346, DEC-2013/09/B/ST6/01535, DEC-2011/03/B/ST6/00346 and DEC-2013/09/N/ST6/01170","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G7246022940","display_name":null,"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/G8521439554","display_name":null,"funder_award_id":"EP/L012138/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1483892218","https://openalex.org/W1484900789","https://openalex.org/W1518197906","https://openalex.org/W1536964483","https://openalex.org/W1573061520","https://openalex.org/W1577924337","https://openalex.org/W1579865136","https://openalex.org/W1584587517","https://openalex.org/W1816620374","https://openalex.org/W1983524017","https://openalex.org/W1991981864","https://openalex.org/W1992955510","https://openalex.org/W1997160698","https://openalex.org/W1998698985","https://openalex.org/W2005612348","https://openalex.org/W2017018565","https://openalex.org/W2025535135","https://openalex.org/W2030359223","https://openalex.org/W2036564813","https://openalex.org/W2053455078","https://openalex.org/W2119397055","https://openalex.org/W2123205690","https://openalex.org/W2124580444","https://openalex.org/W2131159347","https://openalex.org/W2246583867","https://openalex.org/W2292983454","https://openalex.org/W2295240344","https://openalex.org/W2611888112"],"related_works":["https://openalex.org/W2040509999","https://openalex.org/W1486715727","https://openalex.org/W2743317844","https://openalex.org/W2041536784","https://openalex.org/W2594077579","https://openalex.org/W1978299898","https://openalex.org/W2147888141","https://openalex.org/W85597501","https://openalex.org/W2020230082","https://openalex.org/W1536883094"],"abstract_inverted_index":{"Verification":[0],"of":[1,8,19,95,106,109,120,144,155,171,175,185,193],"properties":[2],"expressed":[3],"in":[4,16,173],"the":[5,50,69,107,116,131,135,142,183,188,191],"two-variable":[6],"fragment":[7],"first-order":[9],"logic":[10],"FO":[11,25,44,66,87,96,110,156,176,199],"2":[12,26,45,67,88,97,111,157,163,177,200],"has":[13,68],"been":[14],"investigated":[15],"a":[17,75,90,103,152,194],"number":[18,184],"contexts.":[20],"The":[21],"satisfiability":[22,57,94,197],"problem":[23],"for":[24,79,93,181,198],"over":[27,98,202],"arbitrary":[28],"structures":[29],"is":[30,46,58],"known":[31,47],"to":[32,48,196],"be":[33],"NEXPTIME-complete,":[34],"with":[35],"satisfiable":[36],"formulas":[37],"having":[38],"exponential-sized":[39],"models.":[40,121],"Over":[41,61],"words,":[42],"where":[43],"have":[49],"same":[51,70],"expressiveness":[52,71],"as":[53,72],"unary":[54],"temporal":[55],"logic,":[56],"again":[59],"NEXPTIME-complete.":[60],"finite":[62,203],"labelled":[63],"ordered":[64],"trees,":[65,113],"navigational":[73],"XPath,":[74],"popular":[76],"query":[77],"language":[78],"XML":[80],"documents.":[81],"Prior":[82],"work":[83,101],"on":[84,112,115,130,146,168],"XPath":[85],"and":[86,114,118,141,190],"gives":[89],"2EXPTIME":[91],"bound":[92],"trees.":[99,147,204],"This":[100],"contains":[102],"comprehensive":[104],"analysis":[105,170],"complexity":[108],"size":[117,192],"depth":[119],"We":[122,148],"show":[123],"that":[124],"different":[125],"techniques":[126,180],"are":[127,137],"required":[128],"depending":[129],"vocabulary":[132],"used,":[133],"whether":[134],"trees":[136],"ranked":[138],"or":[139],"unranked,":[140],"encoding":[143],"labels":[145],"also":[149],"look":[150],"at":[151],"natural":[153],"restriction":[154],",":[158],"its":[159],"guarded":[160],"version,":[161],"GF":[162],".":[164],"Our":[165],"results":[166],"depend":[167],"an":[169],"types":[172],"models":[174],"formulas,":[178],"including":[179],"controlling":[182],"distinct":[186],"subtrees,":[187],"depth,":[189],"witness":[195],"sentences":[201]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
