{"id":"https://openalex.org/W2941322157","doi":"https://doi.org/10.1051/ita/2019002","title":"On the length of uncompletable words in unambiguous automata","display_name":"On the length of uncompletable words in unambiguous automata","publication_year":2019,"publication_date":"2019-04-26","ids":{"openalex":"https://openalex.org/W2941322157","doi":"https://doi.org/10.1051/ita/2019002","mag":"2941322157"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2019002","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2019002","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2019/02/ita180036.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"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":"bronze","oa_url":"https://www.rairo-ita.org/articles/ita/pdf/2019/02/ita180036.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061931277","display_name":"Antonio Boccuto","orcid":"https://orcid.org/0000-0003-3795-8856"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Boccuto","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, 06123 Perugia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3795-8856","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043162342","display_name":"Arturo Carpi","orcid":"https://orcid.org/0000-0002-3204-488X"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Arturo Carpi","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, 06123 Perugia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3204-488X","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043162342"],"corresponding_institution_ids":["https://openalex.org/I27483092"],"apc_list":null,"apc_paid":null,"fwci":0.3856,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62145797,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"53","issue":"3-4","first_page":"115","last_page":"123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T11567","display_name":"semigroups and automata theory","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9940000176429749,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9879000186920166,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7239958047866821},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.7132102251052856},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6812312006950378},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.6538999676704407},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5657132863998413},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.5373787879943848},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5229468941688538},{"id":"https://openalex.org/keywords/syntactic-monoid","display_name":"Syntactic monoid","score":0.5204063653945923},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.464286208152771},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.456512451171875},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43552449345588684},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4110291600227356},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16823789477348328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7239958047866821},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7132102251052856},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6812312006950378},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.6538999676704407},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5657132863998413},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.5373787879943848},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5229468941688538},{"id":"https://openalex.org/C119903167","wikidata":"https://www.wikidata.org/wiki/Q3321297","display_name":"Syntactic monoid","level":4,"score":0.5204063653945923},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.464286208152771},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.456512451171875},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43552449345588684},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4110291600227356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16823789477348328},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ita/2019002","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2019002","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2019/02/ita180036.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"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_2019__53_3-4_115_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita/2019002/","pdf_url":null,"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:zenodo.org:190092","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/190092","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1051/ita/2019002","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2019002","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2019/02/ita180036.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W181030226","https://openalex.org/W204546099","https://openalex.org/W590387709","https://openalex.org/W1523845335","https://openalex.org/W1636572489","https://openalex.org/W1667095670","https://openalex.org/W1807511501","https://openalex.org/W1888551009","https://openalex.org/W1973858274","https://openalex.org/W2028432900","https://openalex.org/W2039849141","https://openalex.org/W2040416787","https://openalex.org/W2059007468","https://openalex.org/W2081502327","https://openalex.org/W2122803069","https://openalex.org/W2312771780","https://openalex.org/W2587144143","https://openalex.org/W4206405967","https://openalex.org/W4230862117","https://openalex.org/W4232006565"],"related_works":["https://openalex.org/W51936586","https://openalex.org/W3161268522","https://openalex.org/W3143205136","https://openalex.org/W2071633178","https://openalex.org/W2971508078","https://openalex.org/W2038387119","https://openalex.org/W3201418638","https://openalex.org/W2090238248","https://openalex.org/W2079194245","https://openalex.org/W1991410416"],"abstract_inverted_index":{"This":[0,18],"paper":[1],"deals":[2],"with":[3,22,138],"uncomplete":[4,111],"unambiguous":[5,112,140],"automata.":[6],"In":[7],"this":[8],"setting,":[9],"we":[10,96,131],"investigate":[11],"the":[12,32,102,115,133,161,165,174,181,185,189],"minimal":[13,103,162,182],"length":[14,104,163,183],"of":[15,34,42,52,55,69,83,90,105,109,164,168,176,178,184,188],"uncompletable":[16,107,166,186],"words.":[17],"problem":[19],"is":[20,49,66,127,145,150,170],"connected":[21],"a":[23,39,50,60,67,72,81,122,146],"well-known":[24],"conjecture":[25],"formulated":[26],"by":[27,59,173],"A.":[28],"Restivo.":[29],"We":[30,44,158],"introduce":[31,132],"notion":[33],"relatively":[35,73,123],"maximal":[36,74,124,134,191],"row":[37,75,125,135,192],"for":[38],"suitable":[40],"monoid":[41,51,120],"matrices.":[43],"show":[45],"that,":[46],"if":[47,152,155],"M":[48,70],"{0,":[53],"1}-matrices":[54],"dimension":[56],"n":[57,86],"generated":[58],"set":[61],"S":[62,91],",":[63],"then":[64],"there":[65],"matrix":[68],"containing":[71],"which":[76,126,149],"can":[77],"be":[78],"expressed":[79],"as":[80],"product":[82],"O":[84],"(":[85],"3":[87],")":[88],"matrices":[89],".":[92,143],"As":[93],"an":[94,106,110,139],"application,":[95],"derive":[97],"some":[98],"upper":[99],"bound":[100],"to":[101],"word":[108],"automaton,":[113,148],"in":[114],"case":[116],"that":[117,160],"its":[118],"transformation":[119],"contains":[121],"not":[128],"maximal.":[129],"Finally":[130],"automaton":[136,141],"associated":[137,190],"A":[142,156,169,179],"It":[144],"deterministic":[147],"complete":[151],"and":[153,180],"only":[154],"is.":[157],"prove":[159],"words":[167,187],"polynomially":[171],"bounded":[172],"number":[175],"states":[177],"automaton.":[193]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}