{"id":"https://openalex.org/W2400082414","doi":"https://doi.org/10.4086/toc.2014.v010a014","title":"","display_name":"","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2400082414","doi":"https://doi.org/10.4086/toc.2014.v010a014","mag":"2400082414"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2014.v010a014","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a014","pdf_url":"https://theoryofcomputing.org/articles/v010a014/v010a014.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v010a014/v010a014.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047872044","display_name":"Sangxia Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sangxia Huang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5047872044"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3493,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6772779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"10","issue":"1","first_page":"359","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9986000061035156,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9986000061035156,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983000159263611,"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/T11567","display_name":"semigroups and automata theory","score":0.9901999831199646,"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/soundness","display_name":"Soundness","score":0.6618964076042175},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6544391512870789},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5082568526268005},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.504848062992096},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4820183515548706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4760313332080841},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44885537028312683},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4431207776069641},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07347020506858826}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6618964076042175},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6544391512870789},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5082568526268005},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.504848062992096},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4820183515548706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4760313332080841},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44885537028312683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4431207776069641},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07347020506858826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2014.v010a014","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a014","pdf_url":"https://theoryofcomputing.org/articles/v010a014/v010a014.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2014.v010a014","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a014","pdf_url":"https://theoryofcomputing.org/articles/v010a014/v010a014.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2400082414.pdf","grobid_xml":"https://content.openalex.org/works/W2400082414.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W573138702","https://openalex.org/W1521487341","https://openalex.org/W1530739071","https://openalex.org/W1577891761","https://openalex.org/W1967935161","https://openalex.org/W1970259241","https://openalex.org/W1973898585","https://openalex.org/W1979065044","https://openalex.org/W1991143034","https://openalex.org/W1992068214","https://openalex.org/W1999032440","https://openalex.org/W2008724760","https://openalex.org/W2019578639","https://openalex.org/W2038663599","https://openalex.org/W2055711302","https://openalex.org/W2073029179","https://openalex.org/W2078929687","https://openalex.org/W2081537403","https://openalex.org/W2091921997","https://openalex.org/W2096478102","https://openalex.org/W2115404728","https://openalex.org/W2120358419","https://openalex.org/W2125534993","https://openalex.org/W2126331452","https://openalex.org/W2148352980","https://openalex.org/W2154276597","https://openalex.org/W2162117620","https://openalex.org/W2169488047","https://openalex.org/W2179897858","https://openalex.org/W2621263703","https://openalex.org/W3037538996","https://openalex.org/W4205962651","https://openalex.org/W4226347946","https://openalex.org/W4244547255","https://openalex.org/W4300471124"],"related_works":["https://openalex.org/W13634261","https://openalex.org/W4250462479","https://openalex.org/W56937029","https://openalex.org/W3163509751","https://openalex.org/W958050847","https://openalex.org/W2396405675","https://openalex.org/W175051304","https://openalex.org/W1548499332","https://openalex.org/W1549730417","https://openalex.org/W1994524667"],"abstract_inverted_index":{"For":[0],"every":[1],"integer":[2],"$k":[3],"\\ge":[4],"3$,":[5],"we":[6,40],"prove":[7],"that":[8,22,68],"there":[9],"is":[10,23,78,86,93],"a":[11,33,69],"predicate":[12,70],"$P$":[13],"on":[14,27,71,81,131,151],"$k$":[15,72],"Boolean":[16],"variables":[17,73],"with":[18,37,74,126],"$2^{\\widetilde{O}(k^{1/3})}$":[19],"accepting":[20,76],"assignments":[21,77],"approximation":[24,44,79],"resistant":[25,80],"even":[26],"satisfiable":[28,34,82],"instances.":[29,83],"That":[30],"is,":[31],"given":[32],"CSP":[35],"instance":[36],"constraint":[38],"$P$,":[39],"cannot":[41],"achieve":[42],"better":[43],"ratio":[45],"than":[46],"simply":[47],"picking":[48],"random":[49],"assignments.":[50],"This":[51],"improves":[52],"the":[53,94,132,143,146],"best":[54],"previously":[55],"known":[56],"result":[57],"by":[58,88,106],"H\u00e5stad":[59],"and":[60],"Khot":[61],"(Theory":[62,119],"of":[63,96,103,120,138,145,153],"Computing,":[64,121,154],"2005)":[65],"who":[66],"showed":[67],"$2^{O(k^{1/2})}$":[75],"Our":[84],"construction":[85],"inspired":[87],"several":[89],"recent":[90],"developments.":[91],"One":[92],"idea":[95],"using":[97],"direct":[98],"sums":[99],"to":[100,123],"improve":[101],"soundness":[102],"PCPs,":[104],"developed":[105],"Siu":[107],"On":[108],"Chan":[109],"(STOC":[110],"2013).":[111],"We":[112],"also":[113],"use":[114],"techniques":[115],"from":[116],"Cenny":[117],"Wenner":[118],"2013)":[122],"construct":[124],"PCPs":[125],"perfect":[127],"completeness":[128],"without":[129],"relying":[130],"$d$-to-1":[133],"Conjecture.":[134],"A":[135],"conference":[136],"version":[137],"this":[139],"paper":[140],"appeared":[141],"in":[142],"Proceedings":[144],"45th":[147],"Annual":[148],"ACM":[149],"Symposium":[150],"Theory":[152],"2013.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2016-06-24T00:00:00"}
