{"id":"https://openalex.org/W2104948090","doi":"https://doi.org/10.1002/malq.200410032","title":"Squares of regular languages","display_name":"Squares of regular languages","publication_year":2005,"publication_date":"2005-03-18","ids":{"openalex":"https://openalex.org/W2104948090","doi":"https://doi.org/10.1002/malq.200410032","mag":"2104948090"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410032","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410032","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","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/A5034994647","display_name":"Gerhard Lischke","orcid":null},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gerhard Lischke","raw_affiliation_strings":["Fakulta\u0308t fu\u0308r Mathematik und Informatik, Friedrich-Schiller-Universita\u0308t Jena, Ernst-Abbe-Platz 1\u20134, D-07743 Jena, Germany","Fakult\u00e4t f\u00fcr Mathematik und Informatik, Friedrich-Schiller-Universit\u00e4t Jena, Ernst-Abbe-Platz 1-4, D-07743 Jena, Germany"],"affiliations":[{"raw_affiliation_string":"Fakulta\u0308t fu\u0308r Mathematik und Informatik, Friedrich-Schiller-Universita\u0308t Jena, Ernst-Abbe-Platz 1\u20134, D-07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Friedrich-Schiller-Universit\u00e4t Jena, Ernst-Abbe-Platz 1-4, D-07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034994647"],"corresponding_institution_ids":["https://openalex.org/I76198965"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17106584,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"51","issue":"3","first_page":"299","last_page":"304"},"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":0.9916999936103821,"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/T12029","display_name":"DNA and Biological Computing","score":0.9889000058174133,"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/square","display_name":"Square (algebra)","score":0.7677034139633179},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.759386420249939},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6931876540184021},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.560164749622345},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5454474687576294},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5361400246620178},{"id":"https://openalex.org/keywords/context-free-language","display_name":"Context-free language","score":0.4400589168071747},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3779293894767761},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.3679529130458832},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3469947576522827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24265244603157043},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.211689293384552},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.18734776973724365},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15652796626091003},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.08495089411735535},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.06360399723052979},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05468246340751648},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.05454191565513611},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.03607407212257385}],"concepts":[{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7677034139633179},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.759386420249939},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6931876540184021},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.560164749622345},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5454474687576294},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5361400246620178},{"id":"https://openalex.org/C198838072","wikidata":"https://www.wikidata.org/wiki/Q729271","display_name":"Context-free language","level":3,"score":0.4400589168071747},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3779293894767761},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.3679529130458832},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3469947576522827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24265244603157043},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.211689293384552},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.18734776973724365},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15652796626091003},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.08495089411735535},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.06360399723052979},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05468246340751648},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05454191565513611},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.03607407212257385},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200410032","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410032","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6100000143051147,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W106234322","https://openalex.org/W1523480252","https://openalex.org/W2002089154","https://openalex.org/W2096383042","https://openalex.org/W6633412286"],"related_works":["https://openalex.org/W2950141706","https://openalex.org/W1788369186","https://openalex.org/W2953369983","https://openalex.org/W1965531865","https://openalex.org/W2401586919","https://openalex.org/W1974626062","https://openalex.org/W2053762111","https://openalex.org/W2440791454","https://openalex.org/W4381706435","https://openalex.org/W4297670065"],"abstract_inverted_index":{"The":[0,17],"square":[1,18],"of":[2,9,19,31,38,53],"a":[3,20,48],"language":[4,22,50],"L":[5],"is":[6,45],"the":[7],"set":[8],"all":[10],"words":[11],"pp":[12],"where":[13],"p":[14],"\u2208":[15],"L.":[16],"regular":[21,25,49],"may":[23],"be":[24],"too":[26],"or":[27,29],"context-free":[28],"none":[30],"both.":[32],"We":[33],"give":[34],"characterizations":[35],"for":[36],"each":[37],"these":[39,54],"cases":[40],"and":[41],"show":[42],"that":[43],"it":[44],"decidable":[46],"whether":[47],"has":[51],"one":[52],"properties.":[55],"(\u00a9":[56],"2005":[57],"WILEY-VCH":[58],"Verlag":[59],"GmbH":[60],"&":[61],"Co.":[62],"KGaA,":[63],"Weinheim)":[64]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}