{"id":"https://openalex.org/W4389402682","doi":"https://doi.org/10.4086/toc.2023.v019a007","title":"","display_name":"","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4389402682","doi":"https://doi.org/10.4086/toc.2023.v019a007"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2023.v019a007","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2023.v019a007","pdf_url":"https://theoryofcomputing.org/articles/v019a007/v019a007.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v019a007/v019a007.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yuval Filmus","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yuval Filmus","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071686980","display_name":"Or Meir","orcid":"https://orcid.org/0000-0001-5031-0750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Or Meir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049425955","display_name":"Avishay Tal","orcid":"https://orcid.org/0000-0002-0375-6554"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avishay Tal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16646139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"1","first_page":"1","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9980999827384949,"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":0.9980000257492065,"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/combinatorics","display_name":"Combinatorics","score":0.7174978852272034},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7137592434883118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6912063360214233},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6735031604766846},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5162755846977234},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5116091370582581},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4657121002674103},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.46554598212242126},{"id":"https://openalex.org/keywords/maximum-cut","display_name":"Maximum cut","score":0.4132680892944336},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14340460300445557},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13049030303955078},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1132889986038208},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08793643116950989}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7174978852272034},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7137592434883118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6912063360214233},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6735031604766846},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5162755846977234},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5116091370582581},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4657121002674103},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.46554598212242126},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.4132680892944336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14340460300445557},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13049030303955078},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1132889986038208},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08793643116950989},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2023.v019a007","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2023.v019a007","pdf_url":"https://theoryofcomputing.org/articles/v019a007/v019a007.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2023.v019a007","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2023.v019a007","pdf_url":"https://theoryofcomputing.org/articles/v019a007/v019a007.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G1799556075","display_name":null,"funder_award_id":"1445/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G2957848115","display_name":null,"funder_award_id":"1337/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389402682.pdf"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2036656440","https://openalex.org/W4226347946"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943","https://openalex.org/W2149931498"],"abstract_inverted_index":{"$":[0,2],"\\newcommand{\\ACz}{\\mathsf{AC}^0}":[1],"H\u00e5stad":[3,77],"showed":[4],"that":[5,27,126,138,184,209],"any":[6,65,210],"De":[7,211],"Morgan":[8,212],"formula":[9,45,103,120,213],"(composed":[10],"of":[11,21,76,85,242,255,266,277,284,291],"AND,":[12],"OR":[13],"and":[14,88],"NOT":[15],"gates)":[16],"shrinks":[17,214],"by":[18,215],"a":[19,24,81,170,216,248],"factor":[20,218],"$\\widetilde{O}(p^{2})$":[22],"under":[23,80,190,219],"random":[25,86,92,175,200,221],"restriction":[26],"leaves":[28],"each":[29],"variable":[30],"alive":[31],"independently":[32],"with":[33,169],"probability":[34],"$p$":[35],"[SICOMP,":[36],"1998].":[37],"Using":[38],"this":[39,69,164,285],"result,":[40],"he":[41],"gave":[42],"an":[43,101,108,275],"$\\widetilde{\\Omega}(n^{3})$":[44,102],"size":[46,104,121],"lower":[47,56,62,105,122,229],"bound":[48,63,106,159],"for":[49,64,107,124,150,153,166,238,247],"the":[50,60,73,117,139,155,180,185,227,239,253,264,289,292],"Andreev":[51],"function,":[52],"which,":[53],"up":[54],"to":[55,78,131,179,225,263],"order":[57],"improvements,":[58],"remains":[59],"state-of-the-art":[61],"explicit":[66,109],"function.":[67],"In":[68,134,162,205],"paper,":[70],"we":[71,99,136,207],"extend":[72],"shrinkage":[74,97],"result":[75],"hold":[79],"far":[82],"wider":[83],"family":[84],"restrictions":[87,201],"their":[89],"generalization":[90],"\u2014":[91,192],"projections.":[93],"Based":[94],"on":[95,235],"our":[96,132,220,269],"results,":[98],"obtain":[100],"function":[110,186],"computable":[111],"in":[112,288,295],"$\\ACz$.":[113],"This":[114,245],"improves":[115],"upon":[116],"best":[118],"known":[119],"bounds":[123],"$\\ACz$,":[125],"were":[127],"only":[128],"quadratic":[129,217],"prior":[130],"work.":[133],"addition,":[135],"prove":[137,226],"KRW":[140],"conjecture":[141],"[Karchmer":[142],"et":[143],"al.,":[144],"Computational":[145],"Complexity":[146],"5(3/4),":[147],"1995]":[148],"holds":[149,165],"inner":[151,167],"functions":[152,168],"which":[154],"unweighted":[156],"quantum":[157],"adversary":[158],"is":[160,196],"tight.":[161],"particular,":[163],"tight":[171],"Khrapchenko":[172],"bound.":[173,230],"Our":[174,231],"projections":[176,195],"are":[177],"tailor-made":[178],"function's":[181],"structure":[182,188],"so":[183],"maintains":[187],"even":[189],"projection":[191],"using":[193],"such":[194],"necessary,":[197],"as":[198,274],"standard":[199],"simplify":[202],"$\\ACz$":[203],"circuits.":[204],"contrast,":[206],"show":[208],"projections,":[222],"allowing":[223],"us":[224],"cubic":[228],"proof":[232,237,251,270],"techniques":[233],"build":[234],"H\u00e5stad's":[236,278],"simpler":[240,250],"case":[241,265],"balanced":[243],"formulas.":[244],"allows":[246],"significantly":[249],"at":[252],"cost":[254],"slightly":[256],"worse":[257],"parameters.":[258],"As":[259],"such,":[260],"when":[261],"specialized":[262],"$p$-random":[267],"restrictions,":[268],"can":[271],"be":[272],"used":[273],"exposition":[276],"result.":[279],"-----------------":[280],"An":[281],"extended":[282],"abstract":[283],"article":[286],"appeared":[287],"Proceeding":[290],"12th":[293],"Innovations":[294],"Theoretical":[296],"Computer":[297],"Science":[298],"Conference":[299],"(ITCS'21).":[300]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2023-12-07T00:00:00"}