{"id":"https://openalex.org/W2150560365","doi":"https://doi.org/10.1145/1374376.1374460","title":"Uniform direct product theorems","display_name":"Uniform direct product theorems","publication_year":2008,"publication_date":"2008-05-17","ids":{"openalex":"https://openalex.org/W2150560365","doi":"https://doi.org/10.1145/1374376.1374460","mag":"2150560365"},"language":"en","primary_location":{"id":"doi:10.1145/1374376.1374460","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374460","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5002208831","display_name":"Russell Impagliazzo","orcid":"https://orcid.org/0000-0003-3236-9796"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Russell Impagliazzo","raw_affiliation_strings":["University of California San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075959430","display_name":"Ragesh Jaiswal","orcid":"https://orcid.org/0009-0002-4475-0922"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ragesh Jaiswal","raw_affiliation_strings":["University of California San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066747130","display_name":"Valentine Kabanets","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Valentine Kabanets","raw_affiliation_strings":["Simon Fraser University, Vancouver, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":["Institute of Advanced Studies, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Institute of Advanced Studies, Princeton, NJ, USA","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002208831"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":9.6126,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.98432569,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"579","last_page":"588"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9993000030517578,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9976000189781189,"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/product","display_name":"Product (mathematics)","score":0.6553881168365479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6335163116455078},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6182124614715576},{"id":"https://openalex.org/keywords/direct-product","display_name":"Direct product","score":0.5778864622116089},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5766816735267639},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5634349584579468},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5476776361465454},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5425203442573547},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.542227029800415},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5317225456237793},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5303324460983276},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4891684353351593},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.42353278398513794},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.41916516423225403},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4107673764228821},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.340875506401062},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23069173097610474}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6553881168365479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6335163116455078},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6182124614715576},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.5778864622116089},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5766816735267639},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5634349584579468},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5476776361465454},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5425203442573547},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.542227029800415},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5317225456237793},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5303324460983276},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4891684353351593},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.42353278398513794},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.41916516423225403},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4107673764228821},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.340875506401062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23069173097610474},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1374376.1374460","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374460","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1901622511","https://openalex.org/W1970278864","https://openalex.org/W1973874352","https://openalex.org/W2003159902","https://openalex.org/W2010873187","https://openalex.org/W2021413381","https://openalex.org/W2021736779","https://openalex.org/W2027528470","https://openalex.org/W2049918060","https://openalex.org/W2061106457","https://openalex.org/W2089800914","https://openalex.org/W2103012681","https://openalex.org/W2103539404","https://openalex.org/W2107324709","https://openalex.org/W2108347494","https://openalex.org/W2118541957","https://openalex.org/W2135456059","https://openalex.org/W2160403361","https://openalex.org/W2165743239","https://openalex.org/W2168991396","https://openalex.org/W2294870549","https://openalex.org/W2610313478","https://openalex.org/W2611398525"],"related_works":["https://openalex.org/W1509719224","https://openalex.org/W2728195892","https://openalex.org/W2611822924","https://openalex.org/W2486254595","https://openalex.org/W3204916073","https://openalex.org/W2516690985","https://openalex.org/W2063425181","https://openalex.org/W2055594799","https://openalex.org/W2031906996","https://openalex.org/W2062972911"],"abstract_inverted_index":{"The":[0,250],"classical":[1],"Direct-Product":[2,58],"Theorem":[3,59],"for":[4,72,136,206],"circuits":[5,115,123],"says":[6],"that":[7,71,92,117],"if":[8],"a":[9,52,89,111,169,210,225,246,272,299],"Boolean":[10],"function":[11,32,211,243],"f:":[12],"{0,1}n":[13],"->":[14,37],"{0,1}":[15],"is":[16,39,78,145,256],"somewhat":[17],"hard":[18],"to":[19,42,65,156,182,224,298],"compute":[20,43],"on":[21,44,95,124,129,215,245],"average":[22,45],"by":[23,46,212,259],"small":[24],"circuits,":[25],"then":[26,257],"the":[27,57,85,102,122,125,157,161,237,242,253,263,280,287,305,314],"corresponding":[28],"k-wise":[29],"direct":[30,273,283],"product":[31,284],"fk(x1,...,xk)=(f(x1),...,f(xk))":[33],"(where":[34],"each":[35,142],"xi":[36],"{0,1}n)":[38],"significantly":[40],"harder":[41],"slightly":[47],"smaller":[48],"circuits.":[49],"We":[50,221],"prove":[51],"fully":[53,170],"uniform":[54,171,288],"version":[55,172],"of":[56,100,113,121,134,173,227,241,248,252,262,275,301,316],"with":[60,84,106,153,178,218,293],"information-theoretically":[61],"optimal":[62,179,219,323],"parameters,":[63,180],"up":[64,181],"constant":[66,183,295],"factors.":[67,184],"Namely,":[68],"we":[69,166,232,278],"show":[70],"given":[73],"k":[74],"and":[75,188,268],"\u03b5,":[76],"there":[77],"an":[79,146,200],"efficient":[80,201],"randomized":[81],"algorithm":[82,103,164,205,255],"A":[83,104],"following":[86],"property.":[87],"Given":[88],"circuit":[90,144,148,158],"C":[91],"computes":[93,127],"fk":[94],"at":[96,108,118],"least":[97,109,119],"\u03b5":[98],"fraction":[99,133],"inputs,":[101,135],"outputs":[105],"probability":[107],"3/4":[110],"list":[112,126],"O(1/\u03b5)":[114],"such":[116],"one":[120],"f":[128],"more":[130],"than":[131],"1-\u03b4":[132],"\u03b4":[137],"=":[138],"O((log":[139],"1/\u03b5)/k).":[140],"Moreover,":[141],"output":[143],"AC0":[147],"(of":[149],"size":[150],"poly(n,k,log":[151],"1/\u03b4,1/\u03b5)),":[152],"oracle":[154],"access":[155],"C.":[159],"Using":[160],"Goldreich-Levin":[162],"decoding":[163,254,315],"[5],":[165],"also":[167],"get":[168],"Yao's":[174],"XOR":[175],"Lemma":[176],"[18]":[177],"Our":[185,193],"results":[186],"simplify":[187],"improve":[189],"those":[190],"in":[191,265,286,304],"[10].":[192],"main":[194],"result":[195,285],"may":[196],"be":[197],"viewed":[198],"as":[199],"approximate,":[202],"local,":[203],"list-decoding":[204],"direct-product":[207,229],"codes":[208],"(encoding":[209],"its":[213],"values":[214,240],"all":[216],"k-tuples)":[217],"parameters.":[220],"generalize":[222],"it":[223],"family":[226,267],"\"derandomized\"":[228],"codes,":[230,235,318],"which":[231,319],"call":[233],"intersection":[234],"where":[236],"encoding":[238],"provides":[239],"only":[244,294],"subfamily":[247],"k-tuples.":[249],"quality":[251],"determined":[258],"sampling":[260],"properties":[261],"sets":[264],"this":[266,276,309],"their":[269],"intersections.":[270],"As":[271],"consequence":[274],"generalization":[277],"obtain":[279],"first":[281],"derandomized":[282,324],"setting,":[289],"allowing":[290],"hardness":[291],"amplification":[292],"(as":[296],"opposed":[297],"factor":[300],"k)":[302],"increase":[303],"input":[306],"length.":[307],"Finally,":[308],"general":[310],"setting":[311],"naturally":[312],"allows":[313],"concatenated":[317],"further":[320],"yields":[321],"nearly":[322],"amplification.":[325]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
