{"id":"https://openalex.org/W2012588249","doi":"https://doi.org/10.1142/s0129054110007271","title":"SETS OF K-INDEPENDENT STRINGS","display_name":"SETS OF K-INDEPENDENT STRINGS","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2012588249","doi":"https://doi.org/10.1142/s0129054110007271","mag":"2012588249"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054110007271","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5102821686","display_name":"Yen-Wu Ti","orcid":"https://orcid.org/0000-0003-4241-6971"},"institutions":[{"id":"https://openalex.org/I88780834","display_name":"Hwa Hsia University of Technology","ror":"https://ror.org/02mfjgm25","country_code":"TW","type":"education","lineage":["https://openalex.org/I88780834"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"YEN-WU TI","raw_affiliation_strings":["Dept. Computer Science Information and Engineering, Hwa Hsia Institute of Technology, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"Dept. Computer Science Information and Engineering, Hwa Hsia Institute of Technology, Taipei, Taiwan","institution_ids":["https://openalex.org/I88780834"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043499853","display_name":"Ching-Lueh Chang","orcid":"https://orcid.org/0000-0001-5039-4608"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"funder","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"CHING-LUEH CHANG","raw_affiliation_strings":["Dept. Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"Dept. Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074699028","display_name":"Yuh\u2010Dauh Lyuu","orcid":"https://orcid.org/0000-0003-2079-8825"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"funder","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"YUH-DAUH LYUU","raw_affiliation_strings":["Dept. Computer Science and Information Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106, Taiwan","Dept. Finance, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106, Taiwan"],"affiliations":[{"raw_affiliation_string":"Dept. Computer Science and Information Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106, Taiwan","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"Dept. Finance, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083603294","display_name":"Alexander Shen","orcid":"https://orcid.org/0000-0001-8605-7734"},"institutions":[{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4390039363","display_name":"Infection et inflammation","ror":"https://ror.org/021sh3243","country_code":null,"type":"facility","lineage":["https://openalex.org/I154526488","https://openalex.org/I195731000","https://openalex.org/I277688954","https://openalex.org/I4390039363"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]}],"countries":["FR","RU"],"is_corresponding":false,"raw_author_name":"ALEXANDER SHEN","raw_affiliation_strings":["CNRS & Univ. Aix\u2013Marseille, On leave from IITP RAS, Moscow, Russia","Laboratoire Informatique Fondamentale, Marseille, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Informatique Fondamentale, Marseille, France","institution_ids":["https://openalex.org/I4210115196","https://openalex.org/I4390039363"]},{"raw_affiliation_string":"CNRS & Univ. Aix\u2013Marseille, On leave from IITP RAS, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.885,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"citation_normalized_percentile":{"value":0.634024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":77,"max":79},"biblio":{"volume":"21","issue":"03","first_page":"321","last_page":"327"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997,"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":0.9997,"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":0.9919,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9752,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.81529903},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.47835177},{"id":"https://openalex.org/keywords/independence","display_name":"Independence","score":0.4465355}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.81529903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.68258035},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.64205754},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5865633},{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.58166325},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5641761},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.54935163},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47975457},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.47835177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47739023},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.4465355},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4185827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20266795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054110007271","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":2,"referenced_works":["https://openalex.org/W1638203394","https://openalex.org/W4230960895"],"related_works":["https://openalex.org/W4245395944","https://openalex.org/W3013395906","https://openalex.org/W2168592511","https://openalex.org/W2143551613","https://openalex.org/W2143345456","https://openalex.org/W2138823233","https://openalex.org/W2023236823","https://openalex.org/W2002177687","https://openalex.org/W1979740464","https://openalex.org/W1021180711"],"abstract_inverted_index":{"A":[0],"bit":[1],"string":[2,49],"is":[3,14,20,56,83],"random":[4,26],"(in":[5],"the":[6,38,41,44,51,71,79],"sense":[7],"of":[8,33,40,47,65,68,87,90,97],"algorithmic":[9],"information":[10],"theory)":[11],"if":[12,30,93],"it":[13],"incompressible,":[15],"i.e.,":[16,43],"its":[17,23,59],"Kolmogorov":[18],"complexity":[19,46],"close":[21,57],"to":[22,58,103],"length.":[24,60],"Two":[25],"strings":[27,69,92],"are":[28,100,118],"independent":[29,101],"knowing":[31],"one":[32],"them":[34],"does":[35],"not":[36],"simplify":[37],"description":[39],"other,":[42],"conditional":[45],"each":[48,113],"(using":[50],"other":[52,114],"as":[53],"a":[54,66,88,104],"condition)":[55],"We":[61],"may":[62],"define":[63],"independence":[64],"k-tuple":[67],"in":[70],"same":[72],"way.":[73],"In":[74],"this":[75,98],"paper":[76],"we":[77],"address":[78],"following":[80],"question:":[81],"what":[82],"that":[84,111],"maximal":[85],"cardinality":[86],"set":[89,99],"n-bit":[91],"any":[94],"k":[95],"elements":[96],"(up":[102],"certain":[105],"constant)?":[106],"Lower":[107],"and":[108],"upper":[109],"bounds":[110],"match":[112],"(with":[115],"logarithmic":[116],"precision)":[117],"provided.":[119]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2012588249","counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-04-23T16:08:51.621226","created_date":"2016-06-24"}