{"id":"https://openalex.org/W2619334284","doi":"https://doi.org/10.1145/3065470","title":"Unexpected power of low-depth arithmetic circuits","display_name":"Unexpected power of low-depth arithmetic circuits","publication_year":2017,"publication_date":"2017-05-24","ids":{"openalex":"https://openalex.org/W2619334284","doi":"https://doi.org/10.1145/3065470","mag":"2619334284"},"language":"en","primary_location":{"id":"doi:10.1145/3065470","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3065470","pdf_url":null,"source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"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":"Communications of the ACM","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/A5001183875","display_name":"Ankit Gupta","orcid":"https://orcid.org/0000-0002-5628-3623"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ankit Gupta","raw_affiliation_strings":["Chennai Mathematical Institute, Kelambakkam, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, Kelambakkam, India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112312033","display_name":"Pritish Kamath","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pritish Kamath","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079701530","display_name":"Neeraj Kayal","orcid":null},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Neeraj Kayal","raw_affiliation_strings":["Microsoft Research, Bangalore, India"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Bangalore, India","institution_ids":["https://openalex.org/I4210124949"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070371254","display_name":"Ramprasad Saptharishi","orcid":"https://orcid.org/0000-0002-7485-3220"},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramprasad Saptharishi","raw_affiliation_strings":["Microsoft Research, Bangalore, India"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Bangalore, India","institution_ids":["https://openalex.org/I4210124949"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001183875"],"corresponding_institution_ids":["https://openalex.org/I19149307"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08662128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"6","first_page":"93","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9968000054359436,"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":0.9947999715805054,"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/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.776374340057373},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6872396469116211},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6781629323959351},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6675302386283875},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.6033967733383179},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5739151239395142},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.5596082806587219},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.5503388047218323},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4890185296535492},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4869436025619507},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4856070876121521},{"id":"https://openalex.org/keywords/power-of-two","display_name":"Power of two","score":0.41275182366371155},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.39855343103408813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3681796193122864},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3466866612434387},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32147812843322754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.264045774936676},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.2621142864227295}],"concepts":[{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.776374340057373},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6872396469116211},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6781629323959351},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6675302386283875},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.6033967733383179},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5739151239395142},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.5596082806587219},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.5503388047218323},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4890185296535492},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4869436025619507},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4856070876121521},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.41275182366371155},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.39855343103408813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3681796193122864},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3466866612434387},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32147812843322754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.264045774936676},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.2621142864227295},{"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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3065470","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3065470","pdf_url":null,"source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"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":"Communications of the ACM","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":28,"referenced_works":["https://openalex.org/W1508771701","https://openalex.org/W1527197079","https://openalex.org/W1979337672","https://openalex.org/W1992071680","https://openalex.org/W1998918799","https://openalex.org/W2002803848","https://openalex.org/W2009998423","https://openalex.org/W2016576580","https://openalex.org/W2026036943","https://openalex.org/W2035476608","https://openalex.org/W2044399075","https://openalex.org/W2055425281","https://openalex.org/W2063302961","https://openalex.org/W2069546133","https://openalex.org/W2079910744","https://openalex.org/W2081256023","https://openalex.org/W2117300304","https://openalex.org/W2128510017","https://openalex.org/W2136589970","https://openalex.org/W2139434573","https://openalex.org/W2170831059","https://openalex.org/W2171403864","https://openalex.org/W2248038145","https://openalex.org/W2914183794","https://openalex.org/W2951995773","https://openalex.org/W4235718176","https://openalex.org/W4247080677","https://openalex.org/W6824878413"],"related_works":["https://openalex.org/W2056543843","https://openalex.org/W2276907117","https://openalex.org/W2521537240","https://openalex.org/W2571686129","https://openalex.org/W2068275484","https://openalex.org/W2619334284","https://openalex.org/W1975269884","https://openalex.org/W2548334940","https://openalex.org/W1842713424","https://openalex.org/W2963691683"],"abstract_inverted_index":{"Complexity":[0],"theory":[1],"aims":[2],"at":[3],"understanding":[4],"the":[5,13,23,29,46,111,141,145],"\"hardness\"":[6],"of":[7,15,25,45,48,78,90,103,144],"certain":[8],"tasks":[9],"with":[10],"respect":[11],"to":[12,19,32,38,62,70,110,128,140,171],"number":[14,47],"\"basic":[16],"operations\"":[17],"required":[18,113],"perform":[20],"it.":[21],"In":[22,138],"case":[24],"arithmetic":[26,97],"circuit":[27,98,102],"complexity,":[28],"goal":[30],"is":[31,37,60,81],"understand":[33],"how":[34],"hard":[35],"it":[36,59],"compute":[39],"a":[40,83,88,100,115],"formal":[41,92],"polynomial":[42,93],"in":[43,67,114,130,152,164,174],"terms":[44],"additions":[49],"and":[50],"multiplications":[51],"required.":[52],"Several":[53],"earlier":[54],"results":[55],"have":[56],"shown":[57],"that":[58,122,160],"possible":[61,142],"rearrange":[63],"basic":[64],"computational":[65,153],"elements":[66],"surprising":[68],"ways":[69],"give":[71],"more":[72],"efficient":[73,123],"algorithms.":[74],"The":[75],"main":[76],"result":[77,120],"this":[79,148,158],"article":[80],"along":[82],"similar":[84],"vein.":[85],"We":[86],"present":[87],"simulation":[89],"any":[91,161],"computed":[94],"by":[95,99],"an":[96],"shallow":[101,146],"not-much":[104],"larger":[105],"size.":[106,137],"Roughly,":[107],"depth":[108,131],"corresponds":[109],"time":[112],"massively":[116],"parallel":[117],"computation.":[118],"This":[119],"shows":[121],"computations":[124],"can":[125],"be":[126],"speedup":[127],"run":[129],"three,":[132],"while":[133],"requiring":[134],"surprisingly":[135],"low":[136],"addition":[139],"usefulness":[143],"simulations,":[147],"theorem":[149],"has":[150],"implications":[151],"complexity":[154],"lower":[155,166,175],"bounds,":[156],"since":[157],"implies":[159],"small":[162],"improvement":[163],"current":[165],"bound":[167],"approaches":[168],"would":[169],"lead":[170],"dramatic":[172],"advances":[173],"bounds":[176],"research.":[177]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
