{"id":"https://openalex.org/W4386614349","doi":"https://doi.org/10.48550/arxiv.2309.03986","title":"Noisy Computing of the $\\mathsf{OR}$ and $\\mathsf{MAX}$ Functions","display_name":"Noisy Computing of the $\\mathsf{OR}$ and $\\mathsf{MAX}$ Functions","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386614349","doi":"https://doi.org/10.48550/arxiv.2309.03986"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2309.03986","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":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/2309.03986","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031613608","display_name":"Banghua Zhu","orcid":"https://orcid.org/0000-0002-7320-3533"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Banghua","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078096869","display_name":"Ziao Wang","orcid":"https://orcid.org/0000-0002-3633-8463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Ziao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048560270","display_name":"Nadim Ghaddar","orcid":"https://orcid.org/0000-0002-0619-0920"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghaddar, Nadim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034192173","display_name":"Jiantao Jiao","orcid":"https://orcid.org/0000-0003-3766-8031"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiao, Jiantao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100383688","display_name":"Lele Wang","orcid":"https://orcid.org/0000-0002-4077-433X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Lele","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":69},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Active Learning in Machine Learning Research","score":0.9971,"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/T12072","display_name":"Active Learning in Machine Learning Research","score":0.9971,"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/T11321","display_name":"Low-Density Parity-Check and Polar Codes","score":0.994,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":"Combinatorial Optimization and Complexity Theory","score":0.9909,"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/divergence","display_name":"Divergence (linguistics)","score":0.54995245},{"id":"https://openalex.org/keywords/algorithmic-applications","display_name":"Algorithmic Applications","score":0.490589}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6960013},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.58725464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5507624},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.54995245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40030697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34865662},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2309.03986","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":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2309.03986","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2309.03986","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":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4238204885","https://openalex.org/W3002753104","https://openalex.org/W2600246793","https://openalex.org/W2142036596","https://openalex.org/W2077600819","https://openalex.org/W2072657027","https://openalex.org/W2061531152","https://openalex.org/W2007980826","https://openalex.org/W1979597421"],"abstract_inverted_index":{"We":[0,64],"consider":[1,30],"the":[2,31,34,47,50,104,119,125,131],"problem":[3],"of":[4,8,33,37,46,53,70,72],"computing":[5],"a":[6,92],"function":[7,36,52],"$n$":[9,38,54],"variables":[10],"using":[11],"noisy":[12,44,61],"queries,":[13],"where":[14,99],"each":[15],"query":[16],"is":[17,82],"incorrect":[18],"with":[19,91],"some":[20],"fixed":[21],"and":[22,49,85,109,127],"known":[23],"probability":[24,95],"$p":[25],"\\in":[26],"(0,1/2)$.":[27],"Specifically,":[28],"we":[29],"computation":[32],"$\\mathsf{OR}$":[35],"bits":[39],"(where":[40,57],"queries":[41,58,71],"correspond":[42,59],"to":[43,60,87,113],"readings":[45],"bits)":[48],"$\\mathsf{MAX}$":[51],"real":[55],"numbers":[56],"pairwise":[62],"comparisons).":[63],"show":[65],"that":[66],"an":[67],"expected":[68],"number":[69],"\\[":[73],"(1":[74],"\\pm":[75],"o(1))":[76],"\\frac{n\\log":[77],"\\frac{1}{\\delta}}{D_{\\mathsf{KL}}(p":[78],"\\|":[79,101],"1-p)}":[80],"\\]":[81],"both":[83,89,124],"sufficient":[84],"necessary":[86],"compute":[88],"functions":[90],"vanishing":[93],"error":[94],"$\\delta":[96],"=":[97],"o(1)$,":[98],"$D_{\\mathsf{KL}}(p":[100],"1-p)$":[102],"denotes":[103],"Kullback-Leibler":[105],"divergence":[106],"between":[107],"$\\mathsf{Bern}(p)$":[108],"$\\mathsf{Bern}(1-p)$":[110],"distributions.":[111],"Compared":[112],"previous":[114],"work,":[115],"our":[116],"results":[117],"tighten":[118],"dependence":[120],"on":[121],"$p$":[122],"in":[123],"upper":[126],"lower":[128],"bounds":[129],"for":[130],"two":[132],"functions.":[133]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4386614349","counts_by_year":[],"updated_date":"2024-11-15T21:44:55.611472","created_date":"2023-09-12"}