{"id":"https://openalex.org/W1974226306","doi":"https://doi.org/10.1051/ita/2010005","title":"How to build billiard words using decimations","display_name":"How to build billiard words using decimations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1974226306","doi":"https://doi.org/10.1051/ita/2010005","mag":"1974226306"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2010005","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2010005","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ita/2010005.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108475483","display_name":"Jean-Pierre Borel","orcid":null},"institutions":[{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Pierre Borel","raw_affiliation_strings":["XLim, UMR 6172, Universit\u00e9 de Limoges \u2013 CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France; borel@unilim.fr","XLIM UMR 6172 - Universit\u00e9 de Limoges/CNRS - 123 avenue Albert Thomas - 87060 Limoges Cedex France"],"affiliations":[{"raw_affiliation_string":"XLim, UMR 6172, Universit\u00e9 de Limoges \u2013 CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France; borel@unilim.fr","institution_ids":["https://openalex.org/I65806277","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"XLIM UMR 6172 - Universit\u00e9 de Limoges/CNRS - 123 avenue Albert Thomas - 87060 Limoges Cedex France","institution_ids":["https://openalex.org/I65806277","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108475483"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07243836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"44","issue":"1","first_page":"59","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/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/T12029","display_name":"DNA and Biological Computing","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-billiards","display_name":"Dynamical billiards","score":0.984653115272522},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6264400482177734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6220011115074158},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6175083518028259},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6075797080993652},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.603364109992981},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6012186408042908},{"id":"https://openalex.org/keywords/decimation","display_name":"Decimation","score":0.4937637746334076},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.44975537061691284},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.41579416394233704},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3294503092765808},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3266837000846863},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3145814538002014},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29391545057296753},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28875771164894104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17661818861961365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07894819974899292},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.06618869304656982}],"concepts":[{"id":"https://openalex.org/C193605512","wikidata":"https://www.wikidata.org/wiki/Q2903467","display_name":"Dynamical billiards","level":2,"score":0.984653115272522},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6264400482177734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6220011115074158},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6175083518028259},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6075797080993652},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.603364109992981},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6012186408042908},{"id":"https://openalex.org/C173642442","wikidata":"https://www.wikidata.org/wiki/Q1253346","display_name":"Decimation","level":3,"score":0.4937637746334076},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.44975537061691284},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.41579416394233704},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3294503092765808},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3266837000846863},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3145814538002014},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29391545057296753},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28875771164894104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17661818861961365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07894819974899292},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.06618869304656982},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ita/2010005","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2010005","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2010__44_1_59_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2010005/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2010005.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:HAL:hal-00475632v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00475632","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2010, 44 (1), pp.59-77. &#x27E8;10.1051/ita/2010005&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:numdam.org:ITA_2010__44_1_59_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2010005/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2010005.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1974226306.pdf","grobid_xml":"https://content.openalex.org/works/W1974226306.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W164546868","https://openalex.org/W1585333424","https://openalex.org/W1982970845","https://openalex.org/W1985370291","https://openalex.org/W1987374824","https://openalex.org/W2044992869","https://openalex.org/W2054331622","https://openalex.org/W2073116343","https://openalex.org/W2078253875","https://openalex.org/W2170633497","https://openalex.org/W4233403536","https://openalex.org/W4238159413"],"related_works":["https://openalex.org/W2058697418","https://openalex.org/W1627627718","https://openalex.org/W3044371202","https://openalex.org/W4300455649","https://openalex.org/W2296588302","https://openalex.org/W2950705774","https://openalex.org/W1516895917","https://openalex.org/W1977456141","https://openalex.org/W4387031542","https://openalex.org/W4366999279"],"abstract_inverted_index":{"We":[0],"present":[1],"two":[2],"methods":[3],"based":[4],"on":[5,12,28],"decimation":[6],"for":[7,44,52,61],"computing":[8],"finite":[9,14,20],"billiard":[10,21,46],"words":[11,22],"any":[13],"alphabet.":[15],"The":[16,30,37],"first":[17],"method":[18],"computes":[19],"by":[23],"iteration":[24],"of":[25,32],"some":[26],"transformation":[27],"words.":[29,47],"number":[31],"iterations":[33],"is":[34],"explicitly":[35],"bounded.":[36],"second":[38],"one":[39],"gives":[40],"a":[41],"direct":[42],"formula":[43],"the":[45],"Some":[48],"results":[49],"remain":[50],"true":[51],"infinite":[53],"standard":[54],"Sturmian":[55],"words,":[56],"but":[57],"cannot":[58],"be":[59],"used":[60],"computation":[62],"as":[63],"they":[64],"only":[65],"are":[66],"limit":[67],"results.":[68]},"counts_by_year":[{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
