{"id":"https://openalex.org/W2096801634","doi":"https://doi.org/10.1051/ita:2002007","title":"A Fully Equational Proof of Parikh's Theorem","display_name":"A Fully Equational Proof of Parikh's Theorem","publication_year":2002,"publication_date":"2002-04-01","ids":{"openalex":"https://openalex.org/W2096801634","doi":"https://doi.org/10.1051/ita:2002007","mag":"2096801634"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2002007","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2002007","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","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041913577","display_name":"Luca Aceto","orcid":"https://orcid.org/0000-0002-2197-3018"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Luca Aceto","raw_affiliation_strings":["(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr.\u00a0Bajersvej 7E, 9220 Aalborg \u00d8, Denmark; luca@cs.auc.dk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr.\u00a0Bajersvej 7E, 9220 Aalborg \u00d8, Denmark; luca@cs.auc.dk","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n \u00c9sik","raw_affiliation_strings":["Department of Computer Science, University of Szeged, P.O. Box 652, 6701 Szeged, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Szeged, P.O. Box 652, 6701 Szeged, Hungary","institution_ids":["https://openalex.org/I227486990"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016540152","display_name":"Anna Ing\u00f3lfsd\u00f3ttir","orcid":"https://orcid.org/0000-0001-8362-3075"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Anna Ing\u00f3lfsd\u00f3ttir","raw_affiliation_strings":["(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr.\u00a0Bajersvej 7E, 9220 Aalborg \u00d8, Denmark; luca@cs.auc.dk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(asic esearch in omputer cience, Centre of the Danish National Research Foundation), Department of Computer Science, Aalborg University, Fr.\u00a0Bajersvej 7E, 9220 Aalborg \u00d8, Denmark; luca@cs.auc.dk","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1686,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.79008701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"36","issue":"2","first_page":"129","last_page":"153"},"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":0.9987000226974487,"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":0.9973999857902527,"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/idempotence","display_name":"Idempotence","score":0.7441991567611694},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.7312239408493042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6793471574783325},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6325863003730774},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5542511343955994},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4359646141529083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38478097319602966},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3483848571777344}],"concepts":[{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7441991567611694},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.7312239408493042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6793471574783325},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6325863003730774},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5542511343955994},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4359646141529083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38478097319602966},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3483848571777344},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1051/ita:2002007","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2002007","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","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:CiteSeerX.psu:10.1.1.164.2409","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.2409","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.brics.dk//RS/01/28/BRICS-RS-01-28.pdf","raw_type":"text"},{"id":"pmh:oai:numdam.org:ITA_2002__36_2_129_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2002007/","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:pure.atira.dk:publications/5390a310-8092-11db-8b97-000ea68e967b","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/5390a310-8092-11db-8b97-000ea68e967b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aceto, L, Esik, Z & Ingolfsdottir, A 2002, 'A Fully Equational Proof of Parikh's Theorem', Informatique th\u00e9orique et applications (Imprim\u00e9), vol. 36, no. 2, pp. 129-153. < http://www.edpsciences.org/articles/ita/abs/2002/02/ita0215/ita0215.html >","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W137476671","https://openalex.org/W266537895","https://openalex.org/W421997344","https://openalex.org/W1489604388","https://openalex.org/W1540039008","https://openalex.org/W1563218161","https://openalex.org/W1570949334","https://openalex.org/W1572677512","https://openalex.org/W1581140154","https://openalex.org/W1593534415","https://openalex.org/W1607161872","https://openalex.org/W1967181601","https://openalex.org/W1989146600","https://openalex.org/W2002089154","https://openalex.org/W2002309677","https://openalex.org/W2022772583","https://openalex.org/W2043871010","https://openalex.org/W2045173200","https://openalex.org/W2077478451","https://openalex.org/W2109517606","https://openalex.org/W2137249503","https://openalex.org/W2143658255","https://openalex.org/W2148224873","https://openalex.org/W2157390113","https://openalex.org/W2160650760","https://openalex.org/W2163152086","https://openalex.org/W2478453924","https://openalex.org/W4212873186","https://openalex.org/W6600360367"],"related_works":["https://openalex.org/W1594270709","https://openalex.org/W2362786832","https://openalex.org/W2154958691","https://openalex.org/W2049944211","https://openalex.org/W2373496770","https://openalex.org/W2615385948","https://openalex.org/W2007718591","https://openalex.org/W4386468199","https://openalex.org/W2862035520","https://openalex.org/W2292521816"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3],"validity":[4],"of":[5,18,28,31],"Parikh's":[6],"theorem":[7],"for":[8],"context-free":[9],"languages":[10],"depends":[11],"only":[12],"on":[13],"a":[14],"few":[15],"equational":[16],"properties":[17],"least":[19],"pre-fixed":[20],"points.":[21],"Moreover,":[22],"we":[23],"exhibit":[24],"an":[25],"infinite":[26],"basis":[27],"\u03bc-term":[29],"equations":[30],"continuous":[32],"commutative":[33],"idempotent":[34],"semirings.":[35]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}