{"id":"https://openalex.org/W2169043721","doi":"https://doi.org/10.25596/jalc-2005-439","title":"On the Length of the Wadge Hierarchy of \u03c9-Context-Free Languages","display_name":"On the Length of the Wadge Hierarchy of \u03c9-Context-Free Languages","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2169043721","doi":"https://doi.org/10.25596/jalc-2005-439","mag":"2169043721"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.2276","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.2276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0801.0534v1.pdf","raw_type":"text"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0801.0534v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057731005","display_name":"Olivier Finkel","orcid":"https://orcid.org/0000-0002-6461-2941"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Finkel, Olivier","raw_affiliation_strings":["Equipe de Logique Math\u00e9matique, U.F.R. de Math\u00e9matiques, Universit\u00e9 Paris, Paris cedex, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe de Logique Math\u00e9matique, U.F.R. de Math\u00e9matiques, Universit\u00e9 Paris, Paris cedex, France#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5057731005"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"4","first_page":"439","last_page":"464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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/T12002","display_name":"Computability, Logic, AI Algorithms","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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/hierarchy","display_name":"Hierarchy","score":0.6665889620780945},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6251744031906128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6244185566902161},{"id":"https://openalex.org/keywords/context-free-language","display_name":"Context-free language","score":0.5673313140869141},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.4570285677909851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41627237200737},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3975048363208771},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2925163507461548},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.16671127080917358},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.06636714935302734},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.060546815395355225}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6665889620780945},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6251744031906128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6244185566902161},{"id":"https://openalex.org/C198838072","wikidata":"https://www.wikidata.org/wiki/Q729271","display_name":"Context-free language","level":3,"score":0.5673313140869141},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4570285677909851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41627237200737},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3975048363208771},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2925163507461548},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.16671127080917358},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.06636714935302734},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.060546815395355225},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.2276","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.2276","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0801.0534v1.pdf","raw_type":"text"},{"id":"mag:2169043721","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0801.0534v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.25596/jalc-2005-439","is_oa":true,"landing_page_url":"https://doi.org/10.25596/jalc-2005-439","pdf_url":null,"source":{"id":"https://openalex.org/S62907800","display_name":"Journal of automata, languages and combinatorics","issn_l":"1430-189X","issn":["1430-189X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313929","host_organization_name":"University of Giessen","host_organization_lineage":["https://openalex.org/P4310313929"],"host_organization_lineage_names":["University of Giessen"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"mag:2169043721","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0801.0534v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W3130855","https://openalex.org/W15605986","https://openalex.org/W66397878","https://openalex.org/W76842558","https://openalex.org/W164886591","https://openalex.org/W194559767","https://openalex.org/W194774452","https://openalex.org/W1487753205","https://openalex.org/W1507944585","https://openalex.org/W1512373780","https://openalex.org/W1539382740","https://openalex.org/W1555991696","https://openalex.org/W1557288551","https://openalex.org/W1560050980","https://openalex.org/W1560960962","https://openalex.org/W1563982778","https://openalex.org/W1573390320","https://openalex.org/W1584587517","https://openalex.org/W1621948069","https://openalex.org/W1965816875","https://openalex.org/W1974868602","https://openalex.org/W1977229748","https://openalex.org/W2003940577","https://openalex.org/W2037185109","https://openalex.org/W2037955016","https://openalex.org/W2038722538","https://openalex.org/W2040935142","https://openalex.org/W2043998485","https://openalex.org/W2054090612","https://openalex.org/W2066725205","https://openalex.org/W2070641420","https://openalex.org/W2087879437","https://openalex.org/W2091564354","https://openalex.org/W2112562798","https://openalex.org/W2118713151","https://openalex.org/W2146328638","https://openalex.org/W2402104012","https://openalex.org/W2799061192","https://openalex.org/W2913155813","https://openalex.org/W2949700515","https://openalex.org/W3178533367"],"related_works":["https://openalex.org/W2951426193","https://openalex.org/W3178533367","https://openalex.org/W2003802196","https://openalex.org/W1524850644","https://openalex.org/W3102174678","https://openalex.org/W1629488001","https://openalex.org/W3105972993","https://openalex.org/W2187654218","https://openalex.org/W2168287010","https://openalex.org/W1527238007","https://openalex.org/W10167044","https://openalex.org/W2963445013","https://openalex.org/W1499646381","https://openalex.org/W3157513705","https://openalex.org/W2252866477","https://openalex.org/W2961255482","https://openalex.org/W2963486946","https://openalex.org/W1999287632","https://openalex.org/W3101703959","https://openalex.org/W3197391454"],"abstract_inverted_index":{"We":[0,35],"prove":[1],"in":[2],"this":[3],"paper":[4],"that":[5,38],"the":[6,9,18,24,29,52],"length":[7],"of":[8,12,28,32],"Wadge":[10],"hierarchy":[11],"$\\omega$-context-free":[13,43],"languages":[14,50],"is":[15,23],"greater":[16],"than":[17],"Cantor":[19],"ordinal":[20,30],"$\\epsilon_\\omega$,":[21],"which":[22],"$\\omega^{th}$":[25],"fixed":[26],"point":[27],"exponentiation":[31],"base":[33],"$\\omega$.":[34],"show":[36],"also":[37],"there":[39],"exist":[40],"some":[41],"$\\Sigma_$\\omega$^0$-complete":[42],"languages,":[44],"improving":[45],"previous":[46],"results":[47],"on":[48],"w-context-free":[49],"and":[51],"Borel":[53],"hierarchy.":[54]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
