{"id":"https://openalex.org/W2914834722","doi":"https://doi.org/10.1145/3305270","title":"Distribution Testing Lower Bounds via Reductions from Communication Complexity","display_name":"Distribution Testing Lower Bounds via Reductions from Communication Complexity","publication_year":2019,"publication_date":"2019-02-11","ids":{"openalex":"https://openalex.org/W2914834722","doi":"https://doi.org/10.1145/3305270","mag":"2914834722"},"language":"en","primary_location":{"id":"doi:10.1145/3305270","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3305270","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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 Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.17863/cam.104801","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000042413","display_name":"Eric Blais","orcid":"https://orcid.org/0009-0000-5824-9034"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Eric Blais","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071869723","display_name":"Cl\u00e9ment L. Canonne","orcid":"https://orcid.org/0000-0001-7153-5211"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment L. Canonne","raw_affiliation_strings":["Stanford University, Stanford, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074192050","display_name":"Tom Gur","orcid":"https://orcid.org/0000-0001-7864-7013"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tom Gur","raw_affiliation_strings":["University of Warwick, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000042413"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":2.4258,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89745964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"2","first_page":"1","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9973000288009644,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.808742105960846},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6733603477478027},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6505758762359619},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6259140968322754},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.589792013168335},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.570808470249176},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5461782217025757},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.5256838798522949},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5156092047691345},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.460737407207489},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4576406180858612},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45598629117012024},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4402838349342346},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4376753866672516},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4274665117263794},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34413278102874756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31735891103744507},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09075936675071716}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.808742105960846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6733603477478027},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6505758762359619},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6259140968322754},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.589792013168335},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.570808470249176},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5461782217025757},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.5256838798522949},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5156092047691345},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.460737407207489},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4576406180858612},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45598629117012024},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4402838349342346},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4376753866672516},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4274665117263794},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34413278102874756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31735891103744507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09075936675071716},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3305270","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3305270","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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 Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:123464","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/362871","is_oa":false,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/362871","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.17863/cam.104801","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.104801","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.17863/cam.104801","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.104801","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W116944765","https://openalex.org/W200741540","https://openalex.org/W1499500817","https://openalex.org/W1501167079","https://openalex.org/W1538444754","https://openalex.org/W1538452572","https://openalex.org/W1553031635","https://openalex.org/W1575031463","https://openalex.org/W1607297671","https://openalex.org/W1807114442","https://openalex.org/W1915631879","https://openalex.org/W1928529719","https://openalex.org/W1967328230","https://openalex.org/W1970630090","https://openalex.org/W1982918157","https://openalex.org/W2000163531","https://openalex.org/W2002001845","https://openalex.org/W2018925011","https://openalex.org/W2021646111","https://openalex.org/W2025711128","https://openalex.org/W2026480251","https://openalex.org/W2076381458","https://openalex.org/W2100158662","https://openalex.org/W2100732817","https://openalex.org/W2102942501","https://openalex.org/W2104648144","https://openalex.org/W2127090196","https://openalex.org/W2129311580","https://openalex.org/W2130695933","https://openalex.org/W2133174662","https://openalex.org/W2134169350","https://openalex.org/W2138256420","https://openalex.org/W2169956976","https://openalex.org/W2170990775","https://openalex.org/W2187447858","https://openalex.org/W2271461379","https://openalex.org/W2396049940","https://openalex.org/W2407691716","https://openalex.org/W2419768696","https://openalex.org/W2475351935","https://openalex.org/W2496316373","https://openalex.org/W2578286516","https://openalex.org/W2592411267","https://openalex.org/W2742879957","https://openalex.org/W2887289949","https://openalex.org/W2905839814","https://openalex.org/W2928496982","https://openalex.org/W2950228521","https://openalex.org/W2962841567","https://openalex.org/W2962932693","https://openalex.org/W2963232312","https://openalex.org/W2963553954","https://openalex.org/W2963597818","https://openalex.org/W2963608890","https://openalex.org/W2963920131","https://openalex.org/W4205256993"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2338630033","https://openalex.org/W2100732817","https://openalex.org/W2397531432","https://openalex.org/W3021291082"],"abstract_inverted_index":{"We":[0,118,168],"present":[1],"a":[2,12,36,79,86,89,152],"new":[3,54],"methodology":[4],"for":[5],"proving":[6],"distribution":[7,15,45,55],"testing":[8,16,46,56,76],"lower":[9,57,68],"bounds,":[10,58],"establishing":[11],"connection":[13,211],"between":[14],"and":[17,31,91,95,136,215],"the":[18,26,100,104,111,123,145,156,177,180,187,194,198],"simultaneous":[19],"message":[20],"passing":[21],"(SMP)":[22],"communication":[23],"model.":[24],"Extending":[25],"framework":[27],"of":[28,66,103,115,125,130,158,160,179,183,189,197,200,218],"Blais,":[29],"Brody,":[30],"Matulef":[32],"[15],":[33],"we":[34,142],"show":[35,169],"simple":[37,64],"way":[38],"to":[39,44,52,62,78,110,176,212],"reduce":[40],"(private-coin)":[41],"SMP":[42],"problems":[43],"problems.":[47],"This":[48,203],"method":[49],"allows":[50],"us":[51],"prove":[53,143],"as":[59,61,85,164],"well":[60],"provide":[63],"proofs":[65],"known":[67,163],"bounds.":[69],"Our":[70],"main":[71],"result":[72],"is":[73,107,148,173],"concerned":[74],"with":[75],"identity":[77],"specific":[80],"distribution,":[81],"p":[82,116,184,201],",":[83],"given":[84],"parameter.":[87],"In":[88],"recent":[90],"influential":[92],"work,":[93],"Valiant":[94,96],"[55]":[97],"showed":[98],"that":[99,144,170,192],"sample":[101,146],"complexity":[102,124,147],"aforementioned":[105],"problem":[106,127],"closely":[108,174],"related":[109,175],"\u2113":[112],"2/3":[113],"-quasinorm":[114],".":[117,167],"obtain":[119],"alternative":[120],"bounds":[121],"on":[122],"this":[126,171],"in":[128,155,205,224],"terms":[129],"an":[131,209],"arguably":[132],"more":[133],"intuitive":[134],"measure":[135,219],"using":[137],"simpler":[138],"proofs.":[139],"More":[140],"specifically,":[141],"essentially":[149],"determined":[150],"by":[151],"fundamental":[153],"operator":[154],"theory":[157],"interpolation":[159],"Banach":[161],"spaces,":[162],"Peetre\u2019s":[165],"K-functional":[166],"quantity":[172],"size":[178],"effective":[181],"support":[182],"(loosely":[185],"speaking,":[186],"number":[188],"supported":[190],"elements":[191],"constitute":[193],"vast":[195],"majority":[196],"mass":[199],").":[202],"result,":[204],"turn,":[206],"stems":[207],"from":[208],"unexpected":[210],"functional":[213],"analysis":[214],"refined":[216],"concentration":[217],"inequalities,":[220],"which":[221],"arise":[222],"naturally":[223],"our":[225],"reduction.":[226]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}