{"id":"https://openalex.org/W2170370062","doi":"https://doi.org/10.1142/s0129054105003297","title":"INFINITE ITERATED FUNCTION SYSTEMS IN CANTOR SPACE AND THE HAUSDORFF MEASURE OF \u03c9-POWER LANGUAGES","display_name":"INFINITE ITERATED FUNCTION SYSTEMS IN CANTOR SPACE AND THE HAUSDORFF MEASURE OF \u03c9-POWER LANGUAGES","publication_year":2005,"publication_date":"2005-07-05","ids":{"openalex":"https://openalex.org/W2170370062","doi":"https://doi.org/10.1142/s0129054105003297","mag":"2170370062"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054105003297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003297","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_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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5006703246","display_name":"Ludwig Staiger","orcid":"https://orcid.org/0000-0003-3810-9303"},"institutions":[{"id":"https://openalex.org/I68956291","display_name":"Martin Luther University Halle-Wittenberg","ror":"https://ror.org/05gqaka33","country_code":"DE","type":"education","lineage":["https://openalex.org/I68956291"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"LUDWIG STAIGER","raw_affiliation_strings":["Institut f\u00fcr Informatik, Martin-Luther-Universit\u00e4t Halle- Wittenberg, D - 06099 Halle, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Martin-Luther-Universit\u00e4t Halle- Wittenberg, D - 06099 Halle, Germany","institution_ids":["https://openalex.org/I68956291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006703246"],"corresponding_institution_ids":["https://openalex.org/I68956291"],"apc_list":null,"apc_paid":null,"fwci":1.2682,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78289157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"04","first_page":"787","last_page":"802"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9745000004768372,"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":0.9487000107765198,"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/iterated-function-system","display_name":"Iterated function system","score":0.9131313562393188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8215566873550415},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.700222373008728},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.6708460450172424},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5707876682281494},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.5549274682998657},{"id":"https://openalex.org/keywords/cantor-set","display_name":"Cantor set","score":0.5347263813018799},{"id":"https://openalex.org/keywords/cantor-function","display_name":"Cantor function","score":0.5155117511749268},{"id":"https://openalex.org/keywords/limit-set","display_name":"Limit set","score":0.49945616722106934},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.477657675743103},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.4727146327495575},{"id":"https://openalex.org/keywords/outer-measure","display_name":"Outer measure","score":0.46561312675476074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.452401727437973},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.44211119413375854},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43461573123931885},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4310779869556427},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42875492572784424},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"Formal power series","score":0.42440199851989746},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4222361445426941},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.37118449807167053},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.34554165601730347},{"id":"https://openalex.org/keywords/minkowski\u2013bouligand-dimension","display_name":"Minkowski\u2013Bouligand dimension","score":0.2842068672180176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22572165727615356},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.12180235981941223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08606827259063721}],"concepts":[{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.9131313562393188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8215566873550415},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.700222373008728},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.6708460450172424},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5707876682281494},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5549274682998657},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.5347263813018799},{"id":"https://openalex.org/C149701218","wikidata":"https://www.wikidata.org/wiki/Q938883","display_name":"Cantor function","level":3,"score":0.5155117511749268},{"id":"https://openalex.org/C51337361","wikidata":"https://www.wikidata.org/wiki/Q1825444","display_name":"Limit set","level":3,"score":0.49945616722106934},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.477657675743103},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4727146327495575},{"id":"https://openalex.org/C143924541","wikidata":"https://www.wikidata.org/wiki/Q258374","display_name":"Outer measure","level":5,"score":0.46561312675476074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.452401727437973},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.44211119413375854},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43461573123931885},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4310779869556427},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42875492572784424},{"id":"https://openalex.org/C151746172","wikidata":"https://www.wikidata.org/wiki/Q1003025","display_name":"Formal power series","level":3,"score":0.42440199851989746},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4222361445426941},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.37118449807167053},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.34554165601730347},{"id":"https://openalex.org/C101597101","wikidata":"https://www.wikidata.org/wiki/Q2555655","display_name":"Minkowski\u2013Bouligand dimension","level":4,"score":0.2842068672180176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22572165727615356},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.12180235981941223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08606827259063721},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054105003297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003297","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_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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W21026334","https://openalex.org/W134775205","https://openalex.org/W196919032","https://openalex.org/W421997344","https://openalex.org/W1504907986","https://openalex.org/W1525157939","https://openalex.org/W1584587517","https://openalex.org/W1664039392","https://openalex.org/W1964532778","https://openalex.org/W1982137181","https://openalex.org/W1986891141","https://openalex.org/W1998090580","https://openalex.org/W2001496266","https://openalex.org/W2029001366","https://openalex.org/W2042720934","https://openalex.org/W2062443283","https://openalex.org/W2066725205","https://openalex.org/W2080003810","https://openalex.org/W2091519975","https://openalex.org/W2091730056","https://openalex.org/W2093370454","https://openalex.org/W2128192154","https://openalex.org/W2285504929","https://openalex.org/W2745281314","https://openalex.org/W4211174777","https://openalex.org/W4214697395"],"related_works":["https://openalex.org/W2183646061","https://openalex.org/W2050649104","https://openalex.org/W2368145229","https://openalex.org/W298430808","https://openalex.org/W1568725201","https://openalex.org/W2170370062","https://openalex.org/W1493692490","https://openalex.org/W25657204","https://openalex.org/W1613589403","https://openalex.org/W2493464051"],"abstract_inverted_index":{"We":[0],"use":[1],"means":[2],"of":[3,12,14,42,48],"formal":[4],"language":[5],"theory":[6],"to":[7,26,38],"estimate":[8],"the":[9,46],"Hausdorff":[10],"measure":[11],"sets":[13,22,50],"a":[15,40],"certain":[16],"shape":[17],"in":[18,31],"Cantor":[19],"space.":[20],"These":[21],"are":[23,36],"closely":[24],"related":[25],"infinite":[27,54],"iterated":[28,55],"function":[29,56],"systems":[30],"fractal":[32],"geometry.":[33],"Our":[34],"results":[35],"used":[37],"provide":[39],"series":[41],"simple":[43],"examples":[44],"for":[45,53],"non-coincidence":[47],"limit":[49],"and":[51],"attractors":[52],"systems.":[57]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}