{"id":"https://openalex.org/W2055711302","doi":"https://doi.org/10.1137/070681612","title":"Gowers Uniformity, Influence of Variables, and PCPs","display_name":"Gowers Uniformity, Influence of Variables, and PCPs","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2055711302","doi":"https://doi.org/10.1137/070681612","mag":"2055711302"},"language":"en","primary_location":{"id":"doi:10.1137/070681612","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070681612","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5004360801","display_name":"Alex Samorodnitsky","orcid":"https://orcid.org/0000-0001-8643-7948"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alex Samorodnitsky","raw_affiliation_strings":["salex@huji.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"salex@huji.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057752375","display_name":"Luca Trevisan","orcid":"https://orcid.org/0000-0002-6982-8530"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Trevisan","raw_affiliation_strings":["luca@cs.berkeley.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"luca@cs.berkeley.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004360801"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.456,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.94809062,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"1","first_page":"323","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973000288009644,"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/T10237","display_name":"Cryptography and Data Security","score":0.9948999881744385,"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/soundness","display_name":"Soundness","score":0.7712814211845398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6912969350814819},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6887409687042236},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6652740240097046},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5422102212905884},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5253719091415405},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5224123001098633},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.46695858240127563},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.45368775725364685},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.424618661403656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17156225442886353}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.7712814211845398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6912969350814819},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6887409687042236},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6652740240097046},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5422102212905884},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5253719091415405},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5224123001098633},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.46695858240127563},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.45368775725364685},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.424618661403656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17156225442886353},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070681612","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070681612","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1490233153","https://openalex.org/W1523265685","https://openalex.org/W1554682571","https://openalex.org/W1992866589","https://openalex.org/W1993625811","https://openalex.org/W1997855358","https://openalex.org/W1999032440","https://openalex.org/W2019578639","https://openalex.org/W2072077626","https://openalex.org/W2081254453","https://openalex.org/W2087964954","https://openalex.org/W2097673562","https://openalex.org/W2111385661","https://openalex.org/W2125703559","https://openalex.org/W2137118456","https://openalex.org/W2141304880","https://openalex.org/W2143698439","https://openalex.org/W2148352980","https://openalex.org/W2154933482","https://openalex.org/W2168605444","https://openalex.org/W2335400162","https://openalex.org/W2342433841","https://openalex.org/W2611804663","https://openalex.org/W3004537778"],"related_works":["https://openalex.org/W13634261","https://openalex.org/W4250462479","https://openalex.org/W56937029","https://openalex.org/W3163509751","https://openalex.org/W958050847","https://openalex.org/W2396405675","https://openalex.org/W175051304","https://openalex.org/W1549730417","https://openalex.org/W1548499332","https://openalex.org/W1994524667"],"abstract_inverted_index":{"We":[0,14],"study":[1],"the":[2,27,52,55,102,105,110,113,129,161,169,176,183,189],"relation":[3],"of":[4,49,51,79,86,104,112,136,164,171,192],"query":[5,80],"complexity":[6,81],"and":[7,24,36,62,83,108,168,174,201],"soundness":[8,38,56,87],"in":[9,97,134],"probabilistically":[10],"checkable":[11],"proofs":[12],"(PCPs).":[13],"present":[15],"a":[16,68,77,84,123,140,148,158,165,193],"PCP":[17],"verifier":[18,28,78],"for":[19,43,147],"languages":[20],"that":[21,26,65,72,75,127,178],"are":[22,156],"Unique-Games-Hard":[23,146],"such":[25,71],"makes":[29],"q":[30,50,82],"queries,":[31],"has":[32,37,76],"almost":[33],"perfect":[34],"completeness,":[35],"error":[39,57,88],"at":[40],"most":[41],"$2q/2^q+\\varepsilon$":[42],"arbitrarily":[44],"small":[45],"$\\varepsilon>0$.":[46],"For":[47],"values":[48],"form":[53],"$2^t-1$,":[54],"is":[58,67,95,119,145],"$(q+1)/2^q+\\varepsilon$.":[59],"Charikar,":[60],"Makarychev,":[61],"Makarychev":[63],"show":[64,126],"there":[66],"constant":[69,107,150],"$\\beta$":[70],"every":[73],"language":[74],"ratio":[85],"to":[89,101,109],"completeness":[90],"smaller":[91],"than":[92,143],"$\\beta":[93],"q/2^q$":[94],"decidable":[96],"polynomial":[98],"time.":[99],"Up":[100],"value":[103],"multiplicative":[106],"validity":[111],"Unique":[114],"Games":[115],"Conjecture,":[116],"our":[117],"result":[118],"therefore":[120],"tight.":[121],"As":[122],"corollary,":[124],"we":[125],"approximating":[128],"Maximum":[130],"Independent":[131],"Set":[132],"problem":[133],"graphs":[135],"degree":[137],"$\\Delta$":[138],"within":[139],"factor":[141],"better":[142],"$\\Delta/(\\log\\Delta)^\\alpha$":[144],"certain":[149],"$\\alpha>0$.":[151],"Our":[152],"main":[153],"technical":[154],"results":[155],"(i)":[157],"connection":[159,197],"between":[160,198],"Gowers":[162,199],"uniformity":[163,200],"boolean":[166],"function":[167],"influence":[170,202],"its":[172],"variables":[173],"(ii)":[175],"proof":[177],"\u201cGowers":[179],"uniform\u201d":[180],"functions":[181],"pass":[182],"\u201chypergraph":[184],"linearity":[185],"test\u201d":[186],"approximately":[187],"with":[188],"same":[190],"probability":[191],"random":[194],"function.":[195],"The":[196],"might":[203],"have":[204],"other":[205],"applications.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}