{"id":"https://openalex.org/W1989076199","doi":"https://doi.org/10.1137/070702680","title":"Circuit Lower Bounds for Merlin\u2013Arthur Classes","display_name":"Circuit Lower Bounds for Merlin\u2013Arthur Classes","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1989076199","doi":"https://doi.org/10.1137/070702680","mag":"1989076199"},"language":"en","primary_location":{"id":"doi:10.1137/070702680","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070702680","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/A5085864294","display_name":"Rahul Santhanam","orcid":"https://orcid.org/0000-0002-8716-6091"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rahul Santhanam","raw_affiliation_strings":["rsanthan@cs.toronto.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"rsanthan@cs.toronto.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085864294"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6856,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.68738934,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"3","first_page":"1038","last_page":"1061"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9983999729156494,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9900000095367432,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6817832589149475},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6332153677940369},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5844330787658691},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4881771206855774},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.4782756268978119},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42549869418144226},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.42060309648513794},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3790135979652405},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.35860177874565125},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20855271816253662},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09899836778640747},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07530206441879272}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6817832589149475},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6332153677940369},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5844330787658691},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4881771206855774},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.4782756268978119},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42549869418144226},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.42060309648513794},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3790135979652405},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.35860177874565125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20855271816253662},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09899836778640747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07530206441879272}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070702680","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070702680","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W3697511","https://openalex.org/W1748501741","https://openalex.org/W1901622511","https://openalex.org/W1973874352","https://openalex.org/W1988127406","https://openalex.org/W1989978772","https://openalex.org/W1993138363","https://openalex.org/W1996839061","https://openalex.org/W1998918799","https://openalex.org/W2006912660","https://openalex.org/W2009994177","https://openalex.org/W2011758726","https://openalex.org/W2020029222","https://openalex.org/W2024411274","https://openalex.org/W2026036943","https://openalex.org/W2036656440","https://openalex.org/W2043280328","https://openalex.org/W2044021971","https://openalex.org/W2058859323","https://openalex.org/W2060270693","https://openalex.org/W2061106457","https://openalex.org/W2062965695","https://openalex.org/W2069652878","https://openalex.org/W2070678975","https://openalex.org/W2080132708","https://openalex.org/W2082647621","https://openalex.org/W2083237534","https://openalex.org/W2092018479","https://openalex.org/W2092429268","https://openalex.org/W2097206148","https://openalex.org/W2124619161","https://openalex.org/W2125056957","https://openalex.org/W2134409170","https://openalex.org/W2151536080","https://openalex.org/W2151586869","https://openalex.org/W2158747250","https://openalex.org/W2165293955","https://openalex.org/W2169453948","https://openalex.org/W2170831059","https://openalex.org/W2293988196","https://openalex.org/W2296506534","https://openalex.org/W2331432079","https://openalex.org/W2912080987","https://openalex.org/W4212783949","https://openalex.org/W4213042755","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W2013770701","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2319937810","https://openalex.org/W2370435933","https://openalex.org/W2947625790","https://openalex.org/W603099989"],"abstract_inverted_index":{"We":[0,39,65],"show":[1,77],"that":[2,78,101,123],"for":[3,28,111],"each":[4,48],"$k>0$,":[5],"$\\mathsf{MA}/1$":[6,79],"($\\mathsf{MA}$":[7],"with":[8],"1":[9],"bit":[10],"of":[11,17,32,62,88,90,95,108,125,130,137],"advice)":[12],"does":[13,58,103],"not":[14,59,104],"have":[15,60,105],"circuits":[16,61,94,107],"size":[18,63,96,109],"$n^k$.":[19,64,97],"This":[20],"implies":[21,127],"the":[22,29,33,72,128],"first":[23],"superlinear":[24],"circuit":[25],"lower":[26,69],"bounds":[27],"promise":[30],"versions":[31],"classes":[34],"$\\mathsf{MA}$,":[35],"$\\mathsf{AM}$,":[36],"and":[37],"$\\mathsf{ZPP}_{\\parallel}^{\\mathsf{NP}}$.":[38],"extend":[40],"our":[41,68,118],"main":[42,119],"result":[43],"in":[44,55],"several":[45],"ways.":[46],"For":[47],"k,":[49],"we":[50,76,99,121],"give":[51],"an":[52],"explicit":[53],"language":[54],"$(\\mathsf{MA}\\cap\\mathsf{coMA})/1$":[56],"which":[57],"also":[66],"adapt":[67],"bound":[70],"to":[71,117],"average-case":[73],"setting;":[74],"i.e.,":[75],"cannot":[80],"be":[81],"solved":[82],"on":[83],"more":[84],"than":[85],"$1/2+1/n^k$":[86],"fraction":[87],"inputs":[89],"length":[91],"n":[92],"by":[93],"Furthermore,":[98],"prove":[100],"$\\mathsf{MA}$":[102],"arithmetic":[106],"$n^k$":[110],"any":[112],"k.":[113],"As":[114],"a":[115],"corollary":[116],"result,":[120],"obtain":[122],"derandomization":[124],"$\\mathsf{MA}/O(1)$":[126],"existence":[129],"pseudorandom":[131],"generators":[132],"computable":[133],"using":[134],"$O(1)$":[135],"bits":[136],"advice.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
