{"id":"https://openalex.org/W2995201291","doi":"https://doi.org/10.1145/3369939","title":"Toward a General Direct Product Testing Theorem","display_name":"Toward a General Direct Product Testing Theorem","publication_year":2019,"publication_date":"2019-12-16","ids":{"openalex":"https://openalex.org/W2995201291","doi":"https://doi.org/10.1145/3369939","mag":"2995201291"},"language":"en","primary_location":{"id":"doi:10.1145/3369939","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3369939","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"],"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/A5043150895","display_name":"Elazar Goldenberg","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Elazar Goldenberg","raw_affiliation_strings":["Academic College of Tel Aviv\u2013Yaffo, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academic College of Tel Aviv\u2013Yaffo, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210141777"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066903534","display_name":"C. S. Karthik","orcid":null},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Karthik C. S.","raw_affiliation_strings":["Weizmann Institute of Science, Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043150895"],"corresponding_institution_ids":["https://openalex.org/I4210141777"],"apc_list":null,"apc_paid":null,"fwci":0.2021,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58409865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9983999729156494,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/direct-product","display_name":"Direct product","score":0.689203679561615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6451932787895203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6435736417770386},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47991952300071716},{"id":"https://openalex.org/keywords/testability","display_name":"Testability","score":0.4733731150627136},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.44857513904571533},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43835124373435974},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4325134754180908}],"concepts":[{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.689203679561615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6451932787895203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6435736417770386},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47991952300071716},{"id":"https://openalex.org/C51234621","wikidata":"https://www.wikidata.org/wiki/Q2149495","display_name":"Testability","level":2,"score":0.4733731150627136},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.44857513904571533},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43835124373435974},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4325134754180908},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3369939","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3369939","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:alma.01RUT_INST:11739998840004646","is_oa":false,"landing_page_url":"https://scholarship.libraries.rutgers.edu/esploro/outputs/journalArticle/Toward-a-general-direct-product-testing/991031913593204646","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4685344470","display_name":null,"funder_award_id":"ERC-CoG grant 772839","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1970278864","https://openalex.org/W1971801736","https://openalex.org/W1999705592","https://openalex.org/W2003159902","https://openalex.org/W2021413381","https://openalex.org/W2129578811","https://openalex.org/W2161666429","https://openalex.org/W2741519875","https://openalex.org/W2769516254","https://openalex.org/W2805609980","https://openalex.org/W2809340088","https://openalex.org/W2949080915","https://openalex.org/W2963664782","https://openalex.org/W2997346744","https://openalex.org/W6752400976"],"related_works":["https://openalex.org/W2393524141","https://openalex.org/W2365130684","https://openalex.org/W2370255574","https://openalex.org/W2169676947","https://openalex.org/W2906367154","https://openalex.org/W2106502108","https://openalex.org/W2783560053","https://openalex.org/W2098899017","https://openalex.org/W2381807899","https://openalex.org/W2382598150"],"abstract_inverted_index":{"The":[0,173],"direct":[1,50,79,176,255,278,333,347,370],"product":[2,51,80,279,334,348,371],"encoding":[3],"of":[4,175,199,210,229,231,254,266,289,292,356],"a":[5,7,25,30,36,43,57,78,87,107,118,157,170,208,232,258,277,293,298,302,332,346],"string":[6],"\u2208":[8,39,88],"{":[9,63,89],"0,1}":[10,64,90],"n":[11,21,91,245,342,354,358],"on":[12,94,138,145,318],"an":[13],"underlying":[14,129],"domain":[15,268,349,364],"V":[16,28,40,61,105,125,132,134,164,193,225,240,350],"\u2286":[17,351],"(":[18,29,102,106,120,244,352],"k":[19,65,196,243,340,353],"[":[20],"]":[22],")":[23,31,355],"is":[24,70,75,114,166,207,226,301],"function":[26,58],"DP":[27],"that":[32,93,149,322],"gets":[33],"as":[34,115,156,169],"input":[35],"set":[37,163,228],"S":[38,46,97,103,109,121,123],"and":[41,67,141,165,183,187,203,216,269,309,312,341],"outputs":[42],"restricted":[44],"to":[45,71,77,127,168,275],".":[47],"In":[48,247],"the":[49,150,161,195,200,204,211,222,227,252,262,267,270,287,324,361],"testing":[52,280,335],"problem,":[53],"we":[54,99,250,285,344,368],"are":[55],"given":[56],"F":[59,74,101,137],":":[60],"\u2192":[62],",":[66,98,122,135,343,359,365],"our":[68],"goal":[69],"test":[72,113,171,184,205,271,294,299,325],"whether":[73,83],"close":[76],"encoding\u2014that":[81],"is,":[82],"there":[84],"exists":[85],"some":[86,128],"such":[92],"most":[95],"sets":[96],"have":[100],")=DP":[104],")(":[108],").":[110,246],"A":[111],"natural":[112],"follows:":[116],"select":[117],"pair":[119],"\u2032)\u2208":[124],"according":[126],"distribution":[130,152],"over":[131,160,180],"\u00d7":[133],"query":[136],"this":[139,237,248,283],"pair,":[140],"check":[142],"for":[143,221,338,366],"consistency":[144],"their":[146],"intersection.":[147],"Note":[148],"preceding":[151],"may":[153],"be":[154],"viewed":[155],"weighted":[158],"graph":[159,206,213,272,300,326],"vertex":[162],"referred":[167],"graph.":[172,295],"testability":[174,253],"products":[177,256],"was":[178],"studied":[179],"various":[181],"domains":[182],"graphs:":[185],"Dinur":[186,215],"Steurer":[188],"(CCC\u201914)":[189],"analyzed":[190,219],"it":[191,220,306,330],"when":[192],"equals":[194],"-th":[197],"slice":[198],"Boolean":[201],"hypercube":[202],"member":[209],"Johnson":[212],"family.":[214],"Kaufman":[217],"(FOCS\u201917)":[218],"case":[223,238],"where":[224,235],"faces":[230],"Ramanujan":[233],"complex,":[234],"in":[236,257],"\u2223":[239],"\u2223=":[241],"O":[242],"article,":[249],"study":[251],"general":[259],"setting,":[260],"addressing":[261],"question:":[263],"what":[264],"properties":[265,317],"allow":[273],"one":[274],"prove":[276,369],"theorem?":[281],"Towards":[282],"goal,":[284],"introduce":[286],"notion":[288],"coordinate":[290,303,328],"expansion":[291],"Roughly":[296],"speaking,":[297],"expander":[304],"if":[305],"has":[307,313,327],"global":[308],"local":[310],"expansion,":[311,329],"certain":[314],"nice":[315],"intersection":[316],"sampling.":[319],"We":[320],"show":[321],"whenever":[323],"admits":[331],"theorem.":[336],"Additionally,":[337],"every":[339],"provide":[345],"size":[357],"called":[360],"sliding":[362],"window":[363],"which":[367],"testability.":[372]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}