{"id":"https://openalex.org/W1974827405","doi":"https://doi.org/10.1137/s0097539794264809","title":"Boolean Circuits, Tensor Ranks, and Communication Complexity","display_name":"Boolean Circuits, Tensor Ranks, and Communication Complexity","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W1974827405","doi":"https://doi.org/10.1137/s0097539794264809","mag":"1974827405"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794264809","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794264809","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/A5109848440","display_name":"Pavel Pudl\u00e1k","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pavel Pudl\u00e1k","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vojtech R\u00f6dl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061997850","display_name":"Ji\u0159\u0131\u0301 Sgall","orcid":"https://orcid.org/0000-0003-3658-4848"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jir\u00ed Sgall","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109848440"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1288,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.93797044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"3","first_page":"605","last_page":"633"},"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":0.9950000047683716,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9908000230789185,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.8074713349342346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7139626145362854},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.6199679374694824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.606124222278595},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5437700152397156},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5223554372787476},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5212567448616028},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4891493618488312},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.4332507252693176},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4247852563858032},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.4224355220794678},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4150090515613556}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8074713349342346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7139626145362854},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.6199679374694824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.606124222278595},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5437700152397156},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5223554372787476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5212567448616028},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4891493618488312},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.4332507252693176},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4247852563858032},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.4224355220794678},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4150090515613556},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":2,"locations":[{"id":"doi:10.1137/s0097539794264809","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794264809","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.8340","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.8340","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cas.cz/~sgall/ps/ranks.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W131912969","https://openalex.org/W201320490","https://openalex.org/W1496035090","https://openalex.org/W1530008367","https://openalex.org/W1590864168","https://openalex.org/W1597309321","https://openalex.org/W1999678910","https://openalex.org/W2008671178","https://openalex.org/W2023832849","https://openalex.org/W2031414318","https://openalex.org/W2035081987","https://openalex.org/W2041210515","https://openalex.org/W2049815987","https://openalex.org/W2051019379","https://openalex.org/W2054818820","https://openalex.org/W2068871408","https://openalex.org/W2074920973","https://openalex.org/W2079401865","https://openalex.org/W2080295594","https://openalex.org/W2082249316","https://openalex.org/W2096086248","https://openalex.org/W2107998050","https://openalex.org/W2116794057","https://openalex.org/W2146447528","https://openalex.org/W2152069626","https://openalex.org/W2153478982","https://openalex.org/W2155859297","https://openalex.org/W2340787257","https://openalex.org/W2905110430","https://openalex.org/W2912133662"],"related_works":["https://openalex.org/W2128020755","https://openalex.org/W2289649099","https://openalex.org/W3127603781","https://openalex.org/W2394746612","https://openalex.org/W2965298602","https://openalex.org/W2167059462","https://openalex.org/W2016981839","https://openalex.org/W2917327790","https://openalex.org/W4288555402","https://openalex.org/W1529985544"],"abstract_inverted_index":{"We":[0],"investigate":[1],"two":[2],"methods":[3,37],"for":[4,68,72,108,203],"proving":[5,145],"lower":[6,129,148,163,178],"bounds":[7],"on":[8,18,83,118,131,150,165,180,197,223],"the":[9,15,26,29,48,84,88,119,142,151,166,169,181,186,220],"size":[10,152],"of":[11,28,34,81,87,90,92,122,135,144,153,168,171,173,200],"small-depth":[12],"circuits,":[13],"namely":[14],"approaches":[16],"based":[17,222],"multiparty":[19],"communication":[20,70,120,182],"games":[21],"and":[22,32,57,112,175],"algebraic":[23,49],"characterizations":[24],"extending":[25],"concepts":[27,50],"tensor":[30,89,170],"rank":[31,86],"rigidity":[33,167],"matrices.":[35],"Our":[36,59],"are":[38,62,139,216],"combinatorial,":[39],"but":[40],"we":[41],"think":[42],"that":[43,213],"our":[44],"main":[45,60],"contribution":[46],"concerns":[47],"used":[51],"in":[52,189],"this":[53,94,156,211],"area":[54],"(tensor":[55],"ranks":[56],"rigidity).":[58],"results":[61],"following.":[63],"(i)":[64],"An":[65,194],"$o(n)$-bit":[66],"protocol":[67],"a":[69,146,162,177,190],"game":[71],"computing":[73,109,204],"shifts,":[74],"which":[75,138],"also":[76],"gives":[77,103],"an":[78,104,113],"upper":[79,106,116,195],"bound":[80,107,117,130,149,157,164,179,196],"$o(n^2)$":[82],"contact":[85],"multiplication":[91,172],"polynomials;":[93],"disproves":[95],"some":[96],"earlier":[97],"conjectures.":[98],"A":[99,128],"related":[100,140],"probabilistic":[101],"construction":[102],"$o(n)$":[105],"all":[110,209],"permutations":[111],"$O(n\\log\\log":[114],"n)$":[115],"complexity":[121],"pointer":[123],"jumping":[124],"with":[125],"permutations.":[126],"(ii)":[127],"certain":[132],"restricted":[133,191],"circuits":[134,199,215],"depth":[136,201],"2":[137,202],"to":[141,184],"problem":[143],"superlinear":[147],"logarithmic-depth":[154],"circuits;":[155],"has":[158],"interpretations":[159],"both":[160],"as":[161,176],"polynomials":[174],"needed":[183],"compute":[185],"shift":[187],"function":[188],"model.":[192],"(iii)":[193],"Boolean":[198],"shifts":[205],"and,":[206],"more":[207,217],"generally,":[208],"permutations;":[210],"shows":[212],"such":[214],"efficient":[218],"than":[219],"model":[221],"sending":[224],"bits":[225],"along":[226],"vertex-disjoint":[227],"paths.":[228]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}