{"id":"https://openalex.org/W2119867099","doi":"https://doi.org/10.1109/ccc.2002.1004341","title":"The correlation between parity and quadratic polynomials mod 3","display_name":"The correlation between parity and quadratic polynomials mod 3","publication_year":2003,"publication_date":"2003-06-25","ids":{"openalex":"https://openalex.org/W2119867099","doi":"https://doi.org/10.1109/ccc.2002.1004341","mag":"2119867099"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2002.1004341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://math.clarku.edu/%7Efgreen/papers/quad2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063077203","display_name":"F. Green","orcid":null},"institutions":[{"id":"https://openalex.org/I130785548","display_name":"Clark University","ror":"https://ror.org/04123ky43","country_code":"US","type":"education","lineage":["https://openalex.org/I130785548"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F. Green","raw_affiliation_strings":["Dept. of Math. & Comput. Sci., Clark Univ., Worcester, MA, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Math. & Comput. Sci., Clark Univ., Worcester, MA, USA","institution_ids":["https://openalex.org/I130785548"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063077203"],"corresponding_institution_ids":["https://openalex.org/I130785548"],"apc_list":null,"apc_paid":null,"fwci":0.233,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.502149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":70,"max":72},"biblio":{"volume":null,"issue":null,"first_page":"65","last_page":"72"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9992,"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":0.9992,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.999,"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":0.9953,"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/corollary","display_name":"Corollary","score":0.7026653},{"id":"https://openalex.org/keywords/mod","display_name":"Mod","score":0.6939775},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.6465576},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.4108904}],"concepts":[{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7026653},{"id":"https://openalex.org/C29231244","wikidata":"https://www.wikidata.org/wiki/Q865493","display_name":"Mod","level":2,"score":0.6939775},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.692433},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.6465576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6410772},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.61425185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5362311},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4640049},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.43354508},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.4108904},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.3767456},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.33453318},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12099376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.103435814},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.084364295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2002.1004341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.7780","pdf_url":"http://math.clarku.edu/%7Efgreen/papers/quad2.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.7780","pdf_url":"http://math.clarku.edu/%7Efgreen/papers/quad2.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":34,"referenced_works":["https://openalex.org/W1489774662","https://openalex.org/W1969981165","https://openalex.org/W1982026196","https://openalex.org/W1982847801","https://openalex.org/W2009994177","https://openalex.org/W2011861941","https://openalex.org/W2014593388","https://openalex.org/W2017290750","https://openalex.org/W2030728433","https://openalex.org/W2039799663","https://openalex.org/W2041210515","https://openalex.org/W2045924252","https://openalex.org/W2060270693","https://openalex.org/W2060276273","https://openalex.org/W2062223744","https://openalex.org/W2070678975","https://openalex.org/W2078561064","https://openalex.org/W2080210666","https://openalex.org/W2097957732","https://openalex.org/W2104952158","https://openalex.org/W2107998050","https://openalex.org/W2114527013","https://openalex.org/W2116794057","https://openalex.org/W2137407595","https://openalex.org/W2157443379","https://openalex.org/W2158905189","https://openalex.org/W2281668463","https://openalex.org/W2294221698","https://openalex.org/W2613956024","https://openalex.org/W2732251371","https://openalex.org/W2912133662","https://openalex.org/W3151140615","https://openalex.org/W4240781210","https://openalex.org/W4300757861"],"related_works":["https://openalex.org/W4245663696","https://openalex.org/W3013941779","https://openalex.org/W256006353","https://openalex.org/W2482639199","https://openalex.org/W2388301251","https://openalex.org/W2376029318","https://openalex.org/W2271516242","https://openalex.org/W1998970406","https://openalex.org/W1998659141","https://openalex.org/W1986299634"],"abstract_inverted_index":{"We":[0],"prove":[1],"exponentially":[2],"small":[3],"upper":[4],"bounds":[5,112],"on":[6],"the":[7,34,40,49,60,99],"correlation":[8],"between":[9],"parity":[10],"and":[11,42,88],"quadratic":[12],"polynomials":[13],"mod":[14,36,68],"3.":[15],"One":[16],"corollary":[17],"of":[18,29,45,53,63,72,86,98],"this":[19,64],"is":[20,59],"that":[21],"in":[22,39],"order":[23],"to":[24],"compute":[25],"parity,":[26],"circuits":[27],"consisting":[28],"a":[30,83,94],"threshold":[31],"gate":[32],"at":[33,48],"top,":[35],"3":[37],"gates":[38,44],"middle,":[41],"AND":[43],"fan-in":[46,73],"two":[47],"inputs":[50],"must":[51],"be":[52],"size":[54],"2/sup":[55],"/spl":[56],"Omega/(n)/.":[57],"This":[58,77],"first":[61],"result":[62,85],"type":[65],"for":[66],"general":[67],"subcircuits":[69],"with":[70],"ANDs":[71],"greater":[74],"than":[75],"1.":[76],"yields":[78],"an":[79],"exponential":[80,101,110],"improvement":[81],"over":[82],"recent":[84],"Alon":[87],"Beigel":[89],"(2001).":[90],"The":[91,109],"proof":[92],"uses":[93],"novel":[95],"inductive":[96],"estimate":[97],"relevant":[100],"sums":[102],"introduced":[103],"by":[104],"Cai":[105],"et":[106],"al.":[107],"(1996).":[108],"sum":[111],"are":[113],"tight.":[114]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2119867099","counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2024-12-08T23:50:27.820831","created_date":"2016-06-24"}
