{"id":"https://openalex.org/W1919528438","doi":"https://doi.org/10.1145/3055399.3055425","title":"Addition is exponentially harder than counting for shallow monotone circuits","display_name":"Addition is exponentially harder than counting for shallow monotone circuits","publication_year":2017,"publication_date":"2017-06-15","ids":{"openalex":"https://openalex.org/W1919528438","doi":"https://doi.org/10.1145/3055399.3055425","mag":"1919528438"},"language":"en","primary_location":{"id":"doi:10.1145/3055399.3055425","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3055399.3055425","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=3055425&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dl.acm.org/ft_gateway.cfm?id=3055425&type=pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100329834","display_name":"Xi Chen","orcid":"https://orcid.org/0000-0001-5661-515X"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xi Chen","raw_affiliation_strings":["Columbia University, USA","Columbia University-USA"],"affiliations":[{"raw_affiliation_string":"Columbia University, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Columbia University-USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110785998","display_name":"Igor Carboni Oliveira","orcid":null},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Igor C. Oliveira","raw_affiliation_strings":["Charles University in Prague, Czechia","*Charles University in Prague, Czechia"],"affiliations":[{"raw_affiliation_string":"Charles University in Prague, Czechia","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"*Charles University in Prague, Czechia","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014866889","display_name":"Rocco A. Servedio","orcid":"https://orcid.org/0000-0003-2407-543X"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rocco A. Servedio","raw_affiliation_strings":["Columbia University, USA","Columbia University-USA"],"affiliations":[{"raw_affiliation_string":"Columbia University, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Columbia University-USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100329834"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":0.474,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63452232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1232","last_page":"1245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9995999932289124,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.8518900275230408},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.693131685256958},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6799356341362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6717021465301514},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.6171061992645264},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5879287719726562},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5869476199150085},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5678499937057495},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5672494173049927},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5606245398521423},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5198955535888672},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.43482640385627747},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4266819953918457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1642722487449646},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11945858597755432},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1043163537979126},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08887800574302673},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06954726576805115}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8518900275230408},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.693131685256958},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6799356341362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6717021465301514},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.6171061992645264},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5879287719726562},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5869476199150085},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5678499937057495},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5672494173049927},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5606245398521423},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5198955535888672},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.43482640385627747},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4266819953918457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1642722487449646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11945858597755432},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1043163537979126},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08887800574302673},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06954726576805115},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3055399.3055425","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3055399.3055425","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=3055425&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:129361","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Conference Item"},{"id":"pmh:oai:arXiv.org:1508.03061","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.03061","pdf_url":"https://arxiv.org/pdf/1508.03061","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1508.03061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.03061","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1145/3055399.3055425","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3055399.3055425","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=3055425&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1498875312","display_name":"AF: Small:  Learning and Testing Classes of Distributions","funder_award_id":"1319788","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3250067719","display_name":null,"funder_award_id":"CCF-1149257, CCF-1423100, CCF-1319788 and CCF-1420349","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3250453925","display_name":null,"funder_award_id":"2015-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3635233365","display_name":null,"funder_award_id":"200252/2015-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4802441260","display_name":null,"funder_award_id":"CCF-1319788","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5392328797","display_name":null,"funder_award_id":"CCF-1149257","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6269157484","display_name":"AF: Small: Linear and Polynomial Threshold Functions: Structural Analysis and Algorithmic Applications","funder_award_id":"1420349","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6765057400","display_name":"AF: Small: On the Complexity of Optimal Pricing and Mechanism Design","funder_award_id":"1423100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G707414775","display_name":null,"funder_award_id":"CCF-1319788 and CCF-1420349","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8493963506","display_name":null,"funder_award_id":"CCF-1423100","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8700607569","display_name":null,"funder_award_id":"14203","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1919528438.pdf","grobid_xml":"https://content.openalex.org/works/W1919528438.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W108503560","https://openalex.org/W112858668","https://openalex.org/W1495580177","https://openalex.org/W1528486370","https://openalex.org/W1609370892","https://openalex.org/W1862379263","https://openalex.org/W1988790447","https://openalex.org/W1990284858","https://openalex.org/W2012476164","https://openalex.org/W2015950107","https://openalex.org/W2027625417","https://openalex.org/W2050739958","https://openalex.org/W2062929592","https://openalex.org/W2069124970","https://openalex.org/W2076063813","https://openalex.org/W2082035816","https://openalex.org/W2086789740","https://openalex.org/W2097886040","https://openalex.org/W2107998050","https://openalex.org/W2114527013","https://openalex.org/W2116794057","https://openalex.org/W2120013083","https://openalex.org/W2124218043","https://openalex.org/W2147976235","https://openalex.org/W2152772468","https://openalex.org/W2171564145","https://openalex.org/W2503739928","https://openalex.org/W2611287588","https://openalex.org/W4210720364"],"related_works":["https://openalex.org/W2626373194","https://openalex.org/W2768379587","https://openalex.org/W2406032822","https://openalex.org/W2002068271","https://openalex.org/W1623626896","https://openalex.org/W2094783265","https://openalex.org/W2934762734","https://openalex.org/W2942099076","https://openalex.org/W2394746612","https://openalex.org/W2950639145","https://openalex.org/W2026339776","https://openalex.org/W1991009204","https://openalex.org/W1544866824","https://openalex.org/W1608267737","https://openalex.org/W2405004071","https://openalex.org/W3037930063","https://openalex.org/W2167059462","https://openalex.org/W250538733","https://openalex.org/W2982690488","https://openalex.org/W2951995773"],"abstract_inverted_index":{"Let":[0,36],"Addk,N":[1,74],"denote":[2,38],"the":[3,45],"Boolean":[4,46],"function":[5,47,73,81],"which":[6,48],"takes":[7,49],"as":[8,50,78,90,107],"input":[9,51],"k":[10,17],"strings":[11],"of":[12,104],"N":[13],"bits":[14],"each,":[15],"representing":[16],"numbers":[18],"a(1),\u2026,a(k)":[19],"in":[20],"{0,1,\u2026,2N-1},":[21],"and":[22,26,58,62,85],"outputs":[23,59],"1":[24,60],"if":[25,28,61,64],"only":[27,63],"a(1)":[29],"+":[30,32,66,68],"\u2026":[31,67],"a(k)":[33],"\u2265":[34,70],"2N.":[35],"MAJt,n":[37,86],"a":[39,52,79,91],"monotone":[40,80,92,108],"unweighted":[41],"threshold":[42],"gate,":[43],"i.e.,":[44],"single":[53],"string":[54],"x":[55],"\u0395":[56],"{0,1}n":[57],"x1":[65],"xn":[69],"t.":[71],"The":[72],"may":[75,87],"be":[76,88],"viewed":[77,89],"that":[82,94,101],"performs":[83,95],"addition,":[84],"gate":[93],"counting.":[96],"We":[97],"refer":[98],"to":[99],"circuits":[100],"are":[102],"composed":[103],"MAJ":[105],"gates":[106],"majority":[109],"circuits.":[110]},"counts_by_year":[{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}