{"id":"https://openalex.org/W7148351412","doi":"https://doi.org/10.48550/arxiv.2604.00268","title":"The Mystery Deepens: On the Query Complexity of Tarski Fixed Points","display_name":"The Mystery Deepens: On the Query Complexity of Tarski Fixed Points","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7148351412","doi":"https://doi.org/10.48550/arxiv.2604.00268"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.00268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00268","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.00268","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132801786","display_name":"Xi Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Xi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132818377","display_name":"Yuhao Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yuhao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043084405","display_name":"Mihalis Yannakakis","orcid":"https://orcid.org/0000-0003-2857-1860"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yannakakis, Mihalis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5132801786"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.5708000063896179,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.5708000063896179,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.12349999696016312,"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/T11106","display_name":"Data Management and Algorithms","score":0.0738999992609024,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/fixed-point","display_name":"Fixed point","score":0.5929999947547913},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5113999843597412},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4832000136375427},{"id":"https://openalex.org/keywords/least-fixed-point","display_name":"Least fixed point","score":0.47870001196861267},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.34929999709129333},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.3449999988079071},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3319000005722046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7135000228881836},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5929999947547913},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5113999843597412},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4832000136375427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48089998960494995},{"id":"https://openalex.org/C27333817","wikidata":"https://www.wikidata.org/wiki/Q6134913","display_name":"Least fixed point","level":5,"score":0.47870001196861267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39430001378059387},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39430001378059387},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.34929999709129333},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.00268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00268","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.00268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00268","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"give":[1,67],"an":[2,29],"$O(\\log^2":[3],"n)$-query":[4],"algorithm":[5,27,33,50],"for":[6,34,96],"finding":[7],"a":[8,52,68,79],"Tarski":[9,72,97],"fixed":[10,81,98],"point":[11],"over":[12],"the":[13,18,39,71,85],"$4$-dimensional":[14],"lattice":[15],"$[n]^4$,":[16],"matching":[17],"$\u03a9(\\log^2":[19],"n)$":[20],"lower":[21],"bound":[22,43],"of":[23,47],"[EPRY20].":[24],"Additionally,":[25],"our":[26],"yields":[28],"${O(\\log^{\\lceil":[30,44],"(k-1)/3\\rceil+1}":[31],"n)}$-query":[32],"any":[35],"constant":[36],"$k$,":[37],"improving":[38],"previous":[40],"best":[41],"upper":[42],"(k-1)/2\\rceil+1}":[45],"n)}$":[46],"[CL22].":[48],"Our":[49],"uses":[51],"new":[53,94],"framework":[54],"based":[55],"on":[56],"\\emph{safe":[57],"partial-information}":[58],"functions.":[59],"The":[60],"latter":[61],"were":[62],"introduced":[63],"in":[64],"[CLY23]":[65],"to":[66,74,92],"reduction":[69],"from":[70],"problem":[73],"its":[75],"promised":[76],"version":[77],"with":[78],"unique":[80],"point.":[82],"This":[83],"is":[84],"first":[86],"time":[87],"they":[88],"are":[89],"directly":[90],"used":[91],"design":[93],"algorithms":[95],"points.":[99]},"counts_by_year":[],"updated_date":"2026-04-03T16:44:17.987007","created_date":"2026-04-03T00:00:00"}