{"id":"https://openalex.org/W2954573415","doi":"https://doi.org/10.1145/3492338","title":"Approximate Degree, Weight, and Indistinguishability","display_name":"Approximate Degree, Weight, and Indistinguishability","publication_year":2022,"publication_date":"2022-03-04","ids":{"openalex":"https://openalex.org/W2954573415","doi":"https://doi.org/10.1145/3492338","mag":"2954573415"},"language":"en","primary_location":{"id":"doi:10.1145/3492338","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3492338","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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":"ACM Transactions on Computation Theory","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/A5048366509","display_name":"Xuangui Huang","orcid":"https://orcid.org/0000-0003-0249-4203"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xuangui Huang","raw_affiliation_strings":["Northeastern University, Boston, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-0249-4203","affiliations":[{"raw_affiliation_string":"Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072846764","display_name":"Emanuele Viola","orcid":"https://orcid.org/0000-0001-6091-1824"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emanuele Viola","raw_affiliation_strings":["Northeastern University, Boston, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-6091-1824","affiliations":[{"raw_affiliation_string":"Northeastern University, Boston, MA, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048366509"],"corresponding_institution_ids":["https://openalex.org/I12912129"],"apc_list":null,"apc_paid":null,"fwci":0.3017,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.55193979,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"14","issue":"1","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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":0.9991000294685364,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9980000257492065,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.715232253074646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44579434394836426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3720918297767639},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12936252355575562}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.715232253074646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44579434394836426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3720918297767639},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12936252355575562},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3492338","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3492338","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"mag:2954573415","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc26.html#HuangV19","pdf_url":null,"source":{"id":"https://openalex.org/S4306509107","display_name":"Electron. Colloquium Comput. Complex.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1522263593","https://openalex.org/W1859250467","https://openalex.org/W1891181203","https://openalex.org/W1969865855","https://openalex.org/W1981115804","https://openalex.org/W1994423049","https://openalex.org/W2010501977","https://openalex.org/W2019807548","https://openalex.org/W2025070700","https://openalex.org/W2032916024","https://openalex.org/W2057810289","https://openalex.org/W2103012681","https://openalex.org/W2104038652","https://openalex.org/W2107923128","https://openalex.org/W2124500503","https://openalex.org/W2127259150","https://openalex.org/W2129275337","https://openalex.org/W2136899145","https://openalex.org/W2163361804","https://openalex.org/W2166652312","https://openalex.org/W2173499948","https://openalex.org/W2187292610","https://openalex.org/W2397763371","https://openalex.org/W2604511150","https://openalex.org/W2607334149","https://openalex.org/W2740574634","https://openalex.org/W2765127426","https://openalex.org/W2808904471","https://openalex.org/W2949606720","https://openalex.org/W2950519576","https://openalex.org/W2954573415","https://openalex.org/W2956137306","https://openalex.org/W2963248611","https://openalex.org/W2964023662","https://openalex.org/W3099921078","https://openalex.org/W4233413206","https://openalex.org/W6758071083"],"related_works":[],"abstract_inverted_index":{"We":[0,101,321],"prove":[1,102],"that":[2,103,278,324,341],"the":[3,104,227,297,308,348,369],"OR":[4],"function":[5,109],"on":[6,80,110,195,254],"{-1,1\\}":[7],"n":[8,30,39,52,242],"can":[9,116],"be":[10,117],"pointwise":[11,118],"approximated":[12,119],"with":[13,120],"error":[14,121],"\u03b5":[15,62],"by":[16,125],"a":[17,70,126,185],"polynomial":[18,127],"of":[19,128,229,274,351,361,371],"degree":[20,129,365],"O":[21,28],"(":[22,29],"k":[23,36,48,145,160,257,305,315],")":[24],"and":[25,133,289,296],"weight":[26,134],"2":[27],"log":[31,40],"(1/\u03b5)/k)":[32],",":[33,141,236,286,295],"for":[34,46,75,89,142,157,190,204,222,302,313],"any":[35,47,76,143,158,191,255,325],"\u2265":[37],"\u221a":[38],"(1/\u03b5).":[41],"This":[42,153],"result":[43,74,88,98,154,189,203,217,299,310],"is":[44,155,300,311],"tight":[45,59,71,156,171,186,301,312],"\u2264":[49],"(1-\u03a9":[50],"(1))":[51],".":[53,152,165,180,210,268,320,356],"Previous":[54,166],"results":[55,167,224],"were":[56,168],"either":[57,169],"not":[58,170],"or":[60,172],"had":[61,173],"=":[63,176],"\u03a9":[64],"(1).":[65],"In":[66,181],"general,":[67,182],"we":[68,82,183,197,358,374],"obtain":[69,84,184,199],"approximate":[72,86,187,201,364],"degree-weight":[73,87,188,202],"symmetric":[77,192,287],"function.":[78,193],"Building":[79,194],"this,":[81,196],"also":[83,198,322],"an":[85,200],"bounded-width":[90,205,290],"CNF.":[91],"For":[92,211],"these":[93,212],"two":[94,213,326,339],"classes":[95,214],"no":[96,215],"such":[97,216,223],"was":[99,218],"known.":[100,219],"\\(":[105,111,122,130,135,144,159,174,206,233,237,241,247,256,265,275,282,291,304,314,327,334,343,352],"\\mathsf":[106,207,283,292],"{OR}":[107,284],"\\)":[108,115,124,132,140,151,164,179,209,235,239,243,249,258,267,277,285,294,306,319,330,336,345,355],"\\lbrace":[112],"-1,1\\rbrace":[113],"^n":[114],"\\epsilon":[123,175],"O(k)":[131],"2^{O(n":[136],"\\log":[137,149],"(1/\\epsilon)":[138],"/k)}":[139],"\\ge":[146],"\\sqrt":[147],"{n":[148],"(1/\\epsilon)}":[150],"\\le":[161,316],"(1-\\Omega":[162,317],"(1))n":[163,318],"\\Omega":[177],"(1)":[178],"{CNF}":[208,293],"One":[220],"motivation":[221],"comes":[225],"from":[226],"study":[228],"indistinguishability.":[230],"Two":[231],"distributions":[232,332,340],"P":[234],"Q":[238],"over":[240],"-bit":[244],"strings":[245],"are":[246,333,342],"(k,\\delta)":[248,276],"-indistinguishable":[250,331],"if":[251],"their":[252],"projections":[253],"bits":[259],"have":[260],"statistical":[261],"distance":[262],"at":[263],"most":[264],"\\delta":[266,354],"The":[269],"above":[270],"approximations":[271],"give":[272],"values":[273],"suffice":[279],"to":[280,338],"fool":[281],"functions,":[288],"first":[298],"all":[303],"while":[307],"second":[309],"show":[323],"(k,":[328],"\\delta)":[329],"O(n^{k/2}\\delta)":[335],"-close":[337],"(k,0)":[344],"-indistinguishable,":[346],"improving":[347],"previous":[349],"bound":[350],"O(n)^k":[353],"Finally,":[357],"present":[359],"proofs":[360],"some":[362],"known":[363],"lower":[366],"bounds":[367],"in":[368],"language":[370],"indistinguishability,":[372],"which":[373],"find":[375],"more":[376],"intuitive.":[377]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}