{"id":"https://openalex.org/W7164410975","doi":"https://doi.org/10.48550/arxiv.2606.11448","title":"A Unified Lower Bound on the Noisy Query Complexity of Boolean Functions","display_name":"A Unified Lower Bound on the Noisy Query Complexity of Boolean Functions","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W7164410975","doi":"https://doi.org/10.48550/arxiv.2606.11448"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.11448","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11448","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.11448","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062979441","display_name":"Yuzhou Gu","orcid":"https://orcid.org/0000-0002-9187-9190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Yuzhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138409222","display_name":"Xin Li (51274)","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Xin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005932872","display_name":"Yinzhan Xu","orcid":"https://orcid.org/0009-0002-6809-2514"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Yinzhan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8346999883651733,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8346999883651733,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.10329999774694443,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.014499999582767487,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6133999824523926},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6085000038146973},{"id":"https://openalex.org/keywords/boolean-conjunctive-query","display_name":"Boolean conjunctive query","score":0.5453000068664551},{"id":"https://openalex.org/keywords/query-optimization","display_name":"Query optimization","score":0.5146999955177307},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4690000116825104},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4424999952316284},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.39010000228881836},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3682999908924103},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.3303999900817871}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6141999959945679},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6133999824523926},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6085000038146973},{"id":"https://openalex.org/C24755975","wikidata":"https://www.wikidata.org/wiki/Q4943354","display_name":"Boolean conjunctive query","level":5,"score":0.5453000068664551},{"id":"https://openalex.org/C157692150","wikidata":"https://www.wikidata.org/wiki/Q2919848","display_name":"Query optimization","level":2,"score":0.5146999955177307},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4341000020503998},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36000001430511475},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C24028149","wikidata":"https://www.wikidata.org/wiki/Q7094056","display_name":"Online aggregation","level":5,"score":0.319599986076355},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C192028432","wikidata":"https://www.wikidata.org/wiki/Q845739","display_name":"Query language","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C192939062","wikidata":"https://www.wikidata.org/wiki/Q104840822","display_name":"Sargable","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C99016210","wikidata":"https://www.wikidata.org/wiki/Q5488129","display_name":"Query expansion","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30390000343322754},{"id":"https://openalex.org/C6435147","wikidata":"https://www.wikidata.org/wiki/Q5156627","display_name":"Complexity index","level":3,"score":0.2957000136375427},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2865000069141388},{"id":"https://openalex.org/C96563100","wikidata":"https://www.wikidata.org/wiki/Q8037118","display_name":"Worst-case complexity","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.2632000148296356},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.11448","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11448","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.11448","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.11448","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,94,137,205],"study":[1],"the":[2,15,36,72,89,110,115,124,133,153,170,179,200,217],"query":[3,17,35,44,62,135,155,219],"complexity":[4,63,156,220],"of":[5,38,65,76,106,109,157,184,203],"Boolean":[6,111,158],"functions":[7],"$f:":[8],"\\{0,":[9,12],"1\\}^n":[10],"\\rightarrow":[11],"1\\}$":[13],"in":[14,172,178],"noisy":[16,61,154,218],"model":[18],"introduced":[19],"by":[20,123,132],"Feige,":[21],"Raghavan,":[22],"Peleg":[23],"and":[24,168,187],"Upfal":[25],"[SICOMP":[26],"1994].":[27],"In":[28],"this":[29,140,176],"model,":[30],"an":[31,39,181],"algorithm":[32],"can":[33],"adaptively":[34],"bits":[37],"input":[40,92],"vector,":[41],"but":[42],"each":[43],"result":[45],"is":[46,69,114,129],"independently":[47],"flipped":[48],"with":[49,82],"constant":[50,145],"probability":[51,84],"$p":[52],"\\in":[53],"(0,":[54],"1/2)$;":[55],"repeated":[56],"queries":[57,77],"are":[58],"allowed.":[59],"The":[60],"$\\mathsf{N}_p(f)$":[64,101,128],"a":[66,96,144,161],"function":[67],"$f$":[68],"defined":[70],"as":[71],"minimum":[73],"expected":[74],"number":[75],"needed":[78],"to":[79,143,212],"compute":[80],"$f(x)$":[81],"error":[83],"at":[85],"most":[86,147],"$1/3$,":[87],"for":[88,164,221],"worst":[90],"case":[91],"$x$.":[93],"prove":[95],"general":[97,117,209],"lower":[98,118,130,150,210],"bound":[99,119,211],"on":[100,103,152,216],"based":[102],"degree":[104],"statistics":[105],"certain":[107],"subgraphs":[108],"hypercube.":[112],"This":[113],"first":[116],"beyond":[120],"those":[121],"implied":[122],"simple":[125],"observation":[126],"that":[127,139,191],"bounded":[131],"randomized":[134],"complexity.":[136],"show":[138],"recovers":[141],"(up":[142],"factor)":[146],"previously":[148],"known":[149],"bounds":[151,215],"functions,":[159],"providing":[160],"unified":[162],"framework":[163],"understanding":[165],"these":[166],"results":[167],"simplifying":[169],"proofs":[171],"several":[173,222],"cases.":[174],"Furthermore,":[175],"resolves":[177],"affirmative":[180],"open":[182],"problem":[183],"Gu,":[185],"Li":[186],"Xu":[188],"[COLT":[189],"2025]":[190],"$\\mathsf{N}_p(f)":[192],"=":[193],"\u03a9(\\mathsf{I}(f)":[194],"\\log":[195],"\\mathsf{I}(f))$,":[196],"where":[197],"$\\mathsf{I}(f)$":[198],"denotes":[199],"total":[201],"influence":[202],"$f$.":[204],"also":[206],"apply":[207],"our":[208],"obtain":[213],"tight":[214],"new":[223],"functions.":[224]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-12T00:00:00"}