{"id":"https://openalex.org/W2981580809","doi":"https://doi.org/10.3233/fi-2019-1857","title":"Decidability of Several Concepts of Finiteness for Simple Types","display_name":"Decidability of Several Concepts of Finiteness for Simple Types","publication_year":2019,"publication_date":"2019-10-18","ids":{"openalex":"https://openalex.org/W2981580809","doi":"https://doi.org/10.3233/fi-2019-1857","mag":"2981580809"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2019-1857","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2019-1857","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1822/62972","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055205012","display_name":"Jos\u00e9 Esp\u00edrito Santo","orcid":"https://orcid.org/0000-0002-6348-5653"},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Esp\u00edrito Santo","raw_affiliation_strings":["Centro de Matem\u00e1tica, Universidade do Minho, Portugal. jes@math.uminho.pt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Universidade do Minho, Portugal. jes@math.uminho.pt","institution_ids":["https://openalex.org/I99682543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008660701","display_name":"Ralph Matthes","orcid":"https://orcid.org/0000-0002-7299-2411"},"institutions":[{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ralph Matthes","raw_affiliation_strings":["Institut de Recherche en Informatique de Toulouse (IRIT), CNRS and University of Toulouse, France. ralph.matthes@irit.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Informatique de Toulouse (IRIT), CNRS and University of Toulouse, France. ralph.matthes@irit.fr","institution_ids":["https://openalex.org/I4210119061","https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210160189","https://openalex.org/I4210152422","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063925293","display_name":"Lu\u00eds Pinto","orcid":"https://orcid.org/0000-0003-1338-2688"},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Lu\u00eds Pinto","raw_affiliation_strings":["Centro de Matem\u00e1tica, Universidade do Minho, Portugal. luis@math.uminho.pt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Universidade do Minho, Portugal. luis@math.uminho.pt","institution_ids":["https://openalex.org/I99682543"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055205012"],"corresponding_institution_ids":["https://openalex.org/I99682543"],"apc_list":null,"apc_paid":null,"fwci":0.4354,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72673198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"170","issue":"1-3","first_page":"111","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9945999979972839,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9945999979972839,"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/T11567","display_name":"semigroups and automata theory","score":0.9801999926567078,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9789000153541565,"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/decidability","display_name":"Decidability","score":0.9269518852233887},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.8460732698440552},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7532224655151367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7456140518188477},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6676487326622009},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6485039591789246},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5053775906562805},{"id":"https://openalex.org/keywords/emptiness","display_name":"Emptiness","score":0.48332998156547546},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4653393030166626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36987459659576416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2113761305809021}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.9269518852233887},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8460732698440552},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7532224655151367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7456140518188477},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6676487326622009},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6485039591789246},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5053775906562805},{"id":"https://openalex.org/C2779150620","wikidata":"https://www.wikidata.org/wiki/Q1096367","display_name":"Emptiness","level":2,"score":0.48332998156547546},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4653393030166626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36987459659576416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2113761305809021},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3233/fi-2019-1857","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2019-1857","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02119503v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02119503","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":"https://content.iospress.com/articles/fundamenta-informaticae/fi1857","raw_type":"Journal articles"},{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/62972","is_oa":true,"landing_page_url":"http://hdl.handle.net/1822/62972","pdf_url":null,"source":{"id":"https://openalex.org/S4306400354","display_name":"Reposit\u00f3riUM (Universidade do Minho)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99682543","host_organization_name":"University of Minho","host_organization_lineage":["https://openalex.org/I99682543"],"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":"journal article"},{"id":"pmh:oai:repositorium.uminho.pt:1822/62972","is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/62972","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/62972","is_oa":true,"landing_page_url":"http://hdl.handle.net/1822/62972","pdf_url":null,"source":{"id":"https://openalex.org/S4306400354","display_name":"Reposit\u00f3riUM (Universidade do Minho)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99682543","host_organization_name":"University of Minho","host_organization_lineage":["https://openalex.org/I99682543"],"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":"journal article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1494407580","https://openalex.org/W1965602223","https://openalex.org/W2036947136","https://openalex.org/W2123414912","https://openalex.org/W2491817307","https://openalex.org/W2964018350","https://openalex.org/W3105033282"],"related_works":["https://openalex.org/W2024521168","https://openalex.org/W2367752232","https://openalex.org/W2946506817","https://openalex.org/W3121073237","https://openalex.org/W2904964998","https://openalex.org/W2912897424","https://openalex.org/W2323781932","https://openalex.org/W4280582564","https://openalex.org/W4301807744","https://openalex.org/W2087352669"],"abstract_inverted_index":{"If":[0],"we":[1,64],"consider":[2],"as":[3,120],"\"member\"":[4],"of":[5,11,17,29,38,44,50,53,72,77,88,90,94,100,118,125,132,146,167],"a":[6,81,141,173],"simple":[7,32,171,174],"type":[8,175],"the":[9,24,36,39,42,48,51,59,73,86,133,144,147,152,182],"outcome":[10],"any":[12,45],"successful":[13],"(possibly":[14],"infinite)":[15],"run":[16],"bottom-up":[18],"proof":[19,84,101],"search":[20,40,102,149,184],"that":[21,66,80,98,109],"starts":[22],"from":[23],"type,":[25],"then":[26],"several":[27],"concepts":[28,69],"\"finiteness\"":[30],"for":[31,170],"types":[33],"are":[34,70,159],"possible:":[35],"finiteness":[37,43,49],"space,":[41],"member,":[46],"or":[47],"number":[52],"finite":[54],"members":[55],"(in":[56],"other":[57],"words,":[58],"inhabitants).":[60,126],"In":[61],"this":[62,95],"paper":[63],"show":[65],"these":[67],"three":[68],"instances":[71],"same":[74],"parameterized":[75,83],"notion":[76],"finiteness,":[78],"and":[79],"single,":[82],"shows":[85],"decidability":[87,135],"all":[89],"them.":[91],"One":[92],"instance":[93],"result":[96,107],"means":[97],"termination":[99],"is":[103,108,111,116,129,186],"decidable.":[104],"A":[105],"separate":[106],"emptiness":[110,115],"also":[112,139],"decidable":[113],"(where":[114],"absence":[117,124],"\"members\"":[119],"above,":[121],"not":[122],"just":[123],"This":[127],"fact":[128],"an":[130,177],"ingredient":[131],"main":[134],"result,":[136],"but":[137],"it":[138],"has":[140,176],"different":[142],"application,":[143],"definition":[145],"pruned":[148,183],"space":[150,185],"-":[151],"one":[153],"where":[154],"branches":[155],"leading":[156],"to":[157],"failure":[158],"chopped":[160],"off.":[161],"We":[162],"conclude":[163],"with":[164],"our":[165],"version":[166],"Konig's":[168],"lemma":[169],"types:":[172],"infinite":[178],"member":[179],"exactly":[180],"when":[181],"infinite.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-18T08:16:58.900851","created_date":"2019-11-01T00:00:00"}