{"id":"https://openalex.org/W2035556343","doi":"https://doi.org/10.1137/s0097539794268789","title":"Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets","display_name":"Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2035556343","doi":"https://doi.org/10.1137/s0097539794268789","mag":"2035556343"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794268789","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794268789","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/A5111440737","display_name":"Martin Kummer","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I4210119349","display_name":"Karlsruhe University of Education","ror":"https://ror.org/01t1kq612","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210119349"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Kummer","raw_affiliation_strings":["Institut f\u00fcr Logik, Komplexit\u00e4t und Deduktionssysteme, Universit\u00e4t Karlsruhe, D-76128 Karls-ruhe, Germany,","Universit\u00e4t Karlsruhe"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Logik, Komplexit\u00e4t und Deduktionssysteme, Universit\u00e4t Karlsruhe, D-76128 Karls-ruhe, Germany,","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Universit\u00e4t Karlsruhe","institution_ids":["https://openalex.org/I4210119349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111440737"],"corresponding_institution_ids":["https://openalex.org/I102335020","https://openalex.org/I4210119349"],"apc_list":null,"apc_paid":null,"fwci":1.5176,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.8228425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"6","first_page":"1123","last_page":"1143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9836000204086304,"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/kolmogorov-complexity","display_name":"Kolmogorov complexity","score":0.946453332901001},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.770535945892334},{"id":"https://openalex.org/keywords/kolmogorov-structure-function","display_name":"Kolmogorov structure function","score":0.757182240486145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6982394456863403},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5983836650848389},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5823172926902771},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5808464288711548},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5598804354667664},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5204872488975525},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.51726895570755},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.49885988235473633},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4844346344470978},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47480738162994385},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4554448127746582},{"id":"https://openalex.org/keywords/worst-case-complexity","display_name":"Worst-case complexity","score":0.4339945912361145},{"id":"https://openalex.org/keywords/quantum-complexity-theory","display_name":"Quantum complexity theory","score":0.4311996102333069},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.4150238633155823},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.41202178597450256},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.36044245958328247},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2692565321922302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1902543008327484}],"concepts":[{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.946453332901001},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.770535945892334},{"id":"https://openalex.org/C15995199","wikidata":"https://www.wikidata.org/wiki/Q5805968","display_name":"Kolmogorov structure function","level":3,"score":0.757182240486145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6982394456863403},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5983836650848389},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5823172926902771},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5808464288711548},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5598804354667664},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5204872488975525},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.51726895570755},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.49885988235473633},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4844346344470978},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47480738162994385},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4554448127746582},{"id":"https://openalex.org/C96563100","wikidata":"https://www.wikidata.org/wiki/Q8037118","display_name":"Worst-case complexity","level":3,"score":0.4339945912361145},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.4311996102333069},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.4150238633155823},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.41202178597450256},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.36044245958328247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2692565321922302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1902543008327484},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"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":[{"id":"doi:10.1137/s0097539794268789","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794268789","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":[{"id":"https://metadata.un.org/sdg/16","score":0.6800000071525574,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W197550256","https://openalex.org/W623765668","https://openalex.org/W1489508883","https://openalex.org/W1587797581","https://openalex.org/W1638203394","https://openalex.org/W1966098169","https://openalex.org/W1988444355","https://openalex.org/W1997686864","https://openalex.org/W2026318097","https://openalex.org/W2056414301","https://openalex.org/W2128968786","https://openalex.org/W2293341947","https://openalex.org/W2500491642","https://openalex.org/W2574999163","https://openalex.org/W3003623942","https://openalex.org/W4232277851"],"related_works":["https://openalex.org/W2159650158","https://openalex.org/W2327776271","https://openalex.org/W2964237202","https://openalex.org/W2565115296","https://openalex.org/W1834737061","https://openalex.org/W1988772559","https://openalex.org/W2033194803","https://openalex.org/W2035556343","https://openalex.org/W2011465227","https://openalex.org/W981500437"],"abstract_inverted_index":{"The":[0,19,53,108],"way":[1,4],"in":[2,71,122],"which":[3,47,163],"Kolmogorov":[5,27,106,124],"complexity":[6,9,28,78,96,120],"and":[7,40,69,153],"instance":[8,62,95,119],"affect":[10],"properties":[11],"of":[12,29,32,44,56,76,79,82,146],"recursively":[13],"enumerable":[14],"(r.e.)":[15],"sets":[16,34,46],"is":[17,35,59,97,110,128,141,158],"studied.":[18],"well-known":[20],"$2\\log":[21],"n$":[22],"upper":[23],"bound":[24,50,127],"on":[25],"the":[26,41,57,77,94,105,123,136,139],"initial":[30],"segments":[31],"r.e.":[33,45,91,115],"shown":[36],"to":[37,131],"be":[38],"optimal,":[39],"Turing":[42],"degrees":[43],"attain":[48],"this":[49],"are":[51],"characterized.":[52],"main":[54],"part":[55],"paper":[58],"concerned":[60],"with":[61,118],"complexity,":[63],"introduced":[64],"by":[65,112],"Ko,":[66],"Orponen,":[67],"Sch\u00f6ning,":[68],"Watanabe":[70],"1986,":[72],"as":[73,102,104,150],"a":[74,83,159],"measure":[75],"individual":[80],"instances":[81],"decision":[84],"problem.":[85],"They":[86],"conjectured":[87],"that":[88],"for":[89,143,162],"every":[90],"nonrecursive":[92,116],"set,":[93],"infinitely":[98],"often":[99],"at":[100],"least":[101],"high":[103],"complexity.":[107,125],"conjecture":[109,140],"refuted":[111],"constructing":[113],"an":[114,132],"set":[117,161],"logarithmic":[121],"This":[126],"optimal":[129],"up":[130],"additive":[133],"constant.":[134],"In":[135],"other":[137],"extreme,":[138],"established":[142],"many":[144],"classes":[145],"complete":[147],"sets,":[148],"such":[149],"weak-truth-table-complete":[151],"(wtt-complete)":[152],"Q-complete":[154],"sets.":[155],"However,":[156],"there":[157],"Turing-complete":[160],"it":[164],"fails.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
