{"id":"https://openalex.org/W7117319208","doi":"https://doi.org/10.48550/arxiv.2512.21193","title":"Adjusted Kolmogorov Complexity of Binary Words with Empirical Entropy Normalization","display_name":"Adjusted Kolmogorov Complexity of Binary Words with Empirical Entropy Normalization","publication_year":2025,"publication_date":"2025-12-24","ids":{"openalex":"https://openalex.org/W7117319208","doi":"https://doi.org/10.48550/arxiv.2512.21193"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.21193","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21193","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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.21193","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029550725","display_name":"Brani Vidakovi\u0107","orcid":"https://orcid.org/0000-0001-9155-9325"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vidakovic, Brani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5029550725"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8313999772071838,"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":0.8313999772071838,"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":0.03920000046491623,"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":0.03660000115633011,"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":0.9323999881744385},{"id":"https://openalex.org/keywords/kolmogorov-structure-function","display_name":"Kolmogorov structure function","score":0.738099992275238},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.6919000148773193},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5691999793052673},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5273000001907349},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4404999911785126},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4262000024318695},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.41119998693466187},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.39879998564720154}],"concepts":[{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.9323999881744385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7590000033378601},{"id":"https://openalex.org/C15995199","wikidata":"https://www.wikidata.org/wiki/Q5805968","display_name":"Kolmogorov structure function","level":3,"score":0.738099992275238},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6919000148773193},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5691999793052673},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5273000001907349},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46959999203681946},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4404999911785126},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4262000024318695},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.39879998564720154},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3504999876022339},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C82581908","wikidata":"https://www.wikidata.org/wiki/Q575766","display_name":"Kolmogorov\u2013Smirnov test","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.32330000400543213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.2888999879360199},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C18017163","wikidata":"https://www.wikidata.org/wiki/Q13560113","display_name":"Randomness tests","level":3,"score":0.25540000200271606}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.21193","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21193","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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.21193","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.21193","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":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Kolmogorov":[0,54,119],"complexity":[1,47,55,76,96],"of":[2,15,56,63,67,82,109,139],"a":[3,57,126],"finite":[4],"binary":[5,141],"word":[6,58],"reflects":[7],"both":[8],"algorithmic":[9],"structure":[10],"and":[11,33,69,99,123,129,135],"the":[12,19,39,53,60,78,94,110,137],"empirical":[13,61,121],"distribution":[14,66],"symbols":[16],"appearing":[17],"in":[18,125,132,136],"word.":[20],"Words":[21],"with":[22],"symbol":[23,83],"frequencies":[24],"far":[25],"from":[26,77],"one":[27],"half":[28],"have":[29],"smaller":[30],"combinatorial":[31,80],"richness":[32],"therefore":[34],"appear":[35],"less":[36],"complex":[37],"under":[38,90],"standard":[40],"definition.":[41],"In":[42],"this":[43],"paper":[44],"an":[45],"entropy-normalized":[46],"measure":[48,112],"is":[49,113],"introduced":[50],"that":[51,107],"divides":[52],"by":[59],"entropy":[62],"its":[64],"observed":[65],"zeros":[68],"ones.":[70],"This":[71],"adjustment":[72],"isolates":[73],"intrinsic":[74],"descriptive":[75],"purely":[79],"effect":[81],"imbalance.":[84],"For":[85],"Martin":[86],"L\u00f6f":[87],"random":[88],"sequences":[89],"constructive":[91],"exchangeable":[92],"measures,":[93],"adjusted":[95],"grows":[97],"linearly":[98],"converges":[100],"to":[101],"one.":[102],"A":[103],"pathological":[104],"construction":[105],"shows":[106],"regularity":[108],"underlying":[111],"essential.":[114],"The":[115],"proposed":[116],"framework":[117],"connects":[118],"complexity,":[120],"entropy,":[122],"randomness":[124,133],"natural":[127],"manner":[128],"suggests":[130],"applications":[131],"testing":[134],"analysis":[138],"structured":[140],"data.":[142]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-12-26T00:00:00"}
