{"id":"https://openalex.org/W2024776286","doi":"https://doi.org/10.1007/s00224-014-9554-8","title":"Normality and Finite-State Dimension of Liouville Numbers","display_name":"Normality and Finite-State Dimension of Liouville Numbers","publication_year":2014,"publication_date":"2014-06-08","ids":{"openalex":"https://openalex.org/W2024776286","doi":"https://doi.org/10.1007/s00224-014-9554-8","mag":"2024776286"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-014-9554-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-014-9554-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","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/A5047441815","display_name":"Satyadev Nandakumar","orcid":"https://orcid.org/0000-0002-0214-0598"},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Satyadev Nandakumar","raw_affiliation_strings":["Department of Computer Science, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India","Department of Computer Science, Indian Institute of Technology Kanpur, Kanpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India","institution_ids":["https://openalex.org/I94234084"]},{"raw_affiliation_string":"Department of Computer Science, Indian Institute of Technology Kanpur, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051924953","display_name":"Santhosh Kumar Vangapelli","orcid":null},"institutions":[{"id":"https://openalex.org/I2800401362","display_name":"Government of Andhra Pradesh","ror":"https://ror.org/045mrnd19","country_code":"IN","type":"government","lineage":["https://openalex.org/I2800401362"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Santhosh Kumar Vangapelli","raw_affiliation_strings":["Scaleqa, Hyderabad, Andhra Pradesh, India","Scaleqa, Hyderabad, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scaleqa, Hyderabad, Andhra Pradesh, India","institution_ids":["https://openalex.org/I2800401362"]},{"raw_affiliation_string":"Scaleqa, Hyderabad, India#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047441815"],"corresponding_institution_ids":["https://openalex.org/I94234084"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6916,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87453476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"3","first_page":"392","last_page":"402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8210388422012329},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.7455402612686157},{"id":"https://openalex.org/keywords/unit-interval","display_name":"Unit interval","score":0.6669917702674866},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6442884802818298},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.586945116519928},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5454540848731995},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5378835201263428},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.4959047734737396},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4927237331867218},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.4853028655052185},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.46413394808769226},{"id":"https://openalex.org/keywords/normality","display_name":"Normality","score":0.4577876329421997},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.44580191373825073},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.43356335163116455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42309531569480896},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4113459289073944},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4090755581855774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2600714862346649},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06295186281204224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8210388422012329},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.7455402612686157},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.6669917702674866},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6442884802818298},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.586945116519928},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5454540848731995},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5378835201263428},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4959047734737396},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4927237331867218},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.4853028655052185},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.46413394808769226},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.4577876329421997},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.44580191373825073},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.43356335163116455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42309531569480896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4113459289073944},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4090755581855774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2600714862346649},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06295186281204224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00224-014-9554-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-014-9554-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W106589407","https://openalex.org/W1557463835","https://openalex.org/W1601309559","https://openalex.org/W1999989993","https://openalex.org/W2013665528","https://openalex.org/W2019338982","https://openalex.org/W2023757085","https://openalex.org/W2043927415","https://openalex.org/W2046937767","https://openalex.org/W2082201286","https://openalex.org/W2082647537","https://openalex.org/W2104645570","https://openalex.org/W2122962290","https://openalex.org/W2159025283","https://openalex.org/W2295356166","https://openalex.org/W2592570088","https://openalex.org/W2952223823"],"related_works":["https://openalex.org/W2359497841","https://openalex.org/W4293831958","https://openalex.org/W2801567004","https://openalex.org/W2557274167","https://openalex.org/W129571849","https://openalex.org/W3166372913","https://openalex.org/W2769576143","https://openalex.org/W4300189940","https://openalex.org/W4243049440","https://openalex.org/W3152524194"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}