{"id":"https://openalex.org/W2082003776","doi":"https://doi.org/10.1137/0220003","title":"Amplification of Bounded Depth Monotone Read-Once Boolean Formulae","display_name":"Amplification of Bounded Depth Monotone Read-Once Boolean Formulae","publication_year":1991,"publication_date":"1991-02-01","ids":{"openalex":"https://openalex.org/W2082003776","doi":"https://doi.org/10.1137/0220003","mag":"2082003776"},"language":"en","primary_location":{"id":"doi:10.1137/0220003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220003","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/A5113912227","display_name":"Qian Ping Gu","orcid":"https://orcid.org/0009-0008-6605-8615"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qian Ping Gu","raw_affiliation_strings":["Academia Sinica of China, Beijing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Academia Sinica of China, Beijing, China#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088040293","display_name":"Akira Maruoka","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira Maruoka","raw_affiliation_strings":["Tohoku Univ., Aoba, Aramaki Sendai, Japan"],"affiliations":[{"raw_affiliation_string":"Tohoku Univ., Aoba, Aramaki Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113912227"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.43609271,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71994229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"1","first_page":"41","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9970999956130981,"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/T11130","display_name":"Coding theory and cryptography","score":0.9970999956130981,"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":0.9847000241279602,"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/T10237","display_name":"Cryptography and Data Security","score":0.973800003528595,"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/boolean-function","display_name":"Boolean function","score":0.7776720523834229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7664611339569092},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7363932132720947},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7308059334754944},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6120895743370056},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5052757859230042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43903085589408875},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.43081769347190857},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.27560606598854065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09252220392227173},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07543238997459412}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7776720523834229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7664611339569092},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7363932132720947},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7308059334754944},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6120895743370056},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5052757859230042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43903085589408875},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.43081769347190857},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.27560606598854065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09252220392227173},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07543238997459412},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0220003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220003","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2008470071","https://openalex.org/W2014091871","https://openalex.org/W2062196111","https://openalex.org/W2063584607","https://openalex.org/W2296084214"],"related_works":["https://openalex.org/W2003722472","https://openalex.org/W2999312112","https://openalex.org/W1909384579","https://openalex.org/W2952185983","https://openalex.org/W2056017973","https://openalex.org/W2057810289","https://openalex.org/W258677105","https://openalex.org/W2212615093","https://openalex.org/W1976234213","https://openalex.org/W2474705870"],"abstract_inverted_index":{"Let":[0,83],"f":[1,16,62],"be":[2,90,120],"a":[3,91],"Boolean":[4,95,115],"function":[5,12],"from":[6,17],"$\\{0,1\\}^n$":[7],"to":[8,19,65,68,119,160],"$\\{0,1\\}$.":[9],"The":[10],"amplification":[11],"$A_f":[13,24,74,79],"$":[14,44,89,152],"of":[15,93,101,112,142],"$[0,1]$":[18,20],"is":[21,63,117,137,166],"defined":[22],"as":[23],"(p)":[25,75],"=":[26,35,52,54],"\\Pr":[27],"[f({\\bf":[28],"X}_1":[29,39],",":[30,40],"\\cdots":[31,41],",{\\bf":[32,42],"X}_n":[33,43],")":[34],"1]$,":[36],"where":[37],"${\\bf":[38],"are":[45],"independent":[46],"random":[47],"variables":[48],"with":[49,97],"$\\Pr":[50],"[X_i":[51],"1]":[53],"p$":[55],"for":[56],"$1":[57],"\\leqq":[58,60,76],"i":[59],"n$.":[61],"said":[64,118],"amplify":[66,154],"$(p,q)$":[67],"$(p',q')$":[69],"if":[70,73],"and":[71,78,104],"only":[72],"p'$":[77],"(q)":[80],"\\geqq":[81],"q'$.":[82],"$\\Sigma":[84,147],"_d":[85,88,148,151],"\\cup":[86,149],"\\Pi":[87,150],"family":[92],"monotone":[94,143],"formulae":[96,145],"alternating":[98],"d":[99],"levels":[100],"AND":[102],"gates":[103,106],"OR":[105],"each":[107,124],"having":[108],"the":[109,127,140],"same":[110],"number":[111],"fan-ins.":[113],"A":[114],"formula":[116,128],"read":[121],"once":[122],"when":[123],"variable":[125],"in":[126,146],"occurs":[129],"at":[130],"most":[131],"once.":[132],"In":[133],"this":[134],"paper":[135],"it":[136],"proven":[138],"that":[139,153],"size":[141],"read-once":[144],"$(p,p":[155],"+":[156,162],"1":[157,163],"/":[158,164,172,174],"m)$":[159],"$(p',p'":[161],"c)$":[165],"$\\exp":[167],"(\\theta":[168],"((d":[169],"-":[170,176],"m)(m":[171],"c)^{1":[173],"(d":[175],"1)}":[177],"))$":[178],"under":[179],"certain":[180],"conditions.":[181]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}