{"id":"https://openalex.org/W4225476156","doi":"https://doi.org/10.1007/978-3-030-99253-8_14","title":"First-order separation over countable ordinals","display_name":"First-order separation over countable ordinals","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4225476156","doi":"https://doi.org/10.1007/978-3-030-99253-8_14"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-99253-8_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_14.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003426815","display_name":"Thomas Colcombet","orcid":"https://orcid.org/0000-0001-6529-6963"},"institutions":[{"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thomas Colcombet","raw_affiliation_strings":["IRIF, Universit\u00e9 de Paris & CNRS, Paris, France","UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","CNRS - Centre National de la Recherche Scientifique (France)"],"affiliations":[{"raw_affiliation_string":"IRIF, Universit\u00e9 de Paris & CNRS, Paris, France","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","institution_ids":["https://openalex.org/I4210091437","https://openalex.org/I204730241"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112752014","display_name":"Sam van Gool","orcid":null},"institutions":[{"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sam van Gool","raw_affiliation_strings":["IRIF, Universit\u00e9 de Paris & CNRS, Paris, France","CNRS - Centre National de la Recherche Scientifique (France)","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)"],"affiliations":[{"raw_affiliation_string":"IRIF, Universit\u00e9 de Paris & CNRS, Paris, France","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","institution_ids":["https://openalex.org/I4210091437","https://openalex.org/I204730241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063732938","display_name":"R\u00e9mi Morvan","orcid":"https://orcid.org/0000-0002-1418-3405"},"institutions":[{"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/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I4210150317","display_name":"Laboratoire de Biologie et Pharmacologie Appliqu\u00e9e","ror":"https://ror.org/03njrcx45","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210096427","https://openalex.org/I4210150317"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Morvan","raw_affiliation_strings":["\u00c9cole normale sup\u00e9rieure Paris-Saclay, Gif-sur-Yvette, France","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","CNRS - Centre National de la Recherche Scientifique (France)"],"affiliations":[{"raw_affiliation_string":"\u00c9cole normale sup\u00e9rieure Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210150317"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13  - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"UPCit\u00e9 - Universit\u00e9 Paris Cit\u00e9 (85 boulevard Saint-Germain\r\n75006 Paris - France)","institution_ids":["https://openalex.org/I4210091437","https://openalex.org/I204730241"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003426815"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210117673"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.9917,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85587386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"264","last_page":"284"},"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":0.9968000054359436,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9945999979972839,"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/monoid","display_name":"Monoid","score":0.7581037282943726},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7287377119064331},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7247228622436523},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6501089930534363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5458250045776367},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5202618837356567},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.5038213133811951},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49075230956077576},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4852202236652374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4398643672466278},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37737908959388733}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7581037282943726},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7287377119064331},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7247228622436523},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6501089930534363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5458250045776367},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5202618837356567},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.5038213133811951},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49075230956077576},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4852202236652374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4398643672466278},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37737908959388733},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-030-99253-8_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2201.03089","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.03089","pdf_url":"https://arxiv.org/pdf/2201.03089","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03758110v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03758110","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"FoSSaCS 2022, Apr 2022, Munich, Germany. pp.264-284, &#x27E8;10.1007/978-3-030-99253-8_14&#x27E9;","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-04324217v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04324217","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th International Conference Foundations of Software Science and Computation Structures FOSSACS 2022, Apr 2022, Munich, Germany. pp.264-284, &#x27E8;10.1007/978-3-030-99253-8_14&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-99253-8_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_14.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G794676242","display_name":null,"funder_award_id":"ANR-16-CE40-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225476156.pdf","grobid_xml":"https://content.openalex.org/works/W4225476156.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W157114451","https://openalex.org/W1049919373","https://openalex.org/W1494501847","https://openalex.org/W1533496401","https://openalex.org/W1540540181","https://openalex.org/W1560463521","https://openalex.org/W1606781638","https://openalex.org/W1967376291","https://openalex.org/W1975463147","https://openalex.org/W1981565742","https://openalex.org/W1983547737","https://openalex.org/W2004710041","https://openalex.org/W2019932899","https://openalex.org/W2032475218","https://openalex.org/W2046268252","https://openalex.org/W2062792526","https://openalex.org/W2085467680","https://openalex.org/W2086359902","https://openalex.org/W2116250539","https://openalex.org/W2158441292","https://openalex.org/W2162583406","https://openalex.org/W2272346406","https://openalex.org/W2541640833","https://openalex.org/W2744327158","https://openalex.org/W2963128734","https://openalex.org/W2963690445","https://openalex.org/W2964137219","https://openalex.org/W2964318531","https://openalex.org/W3101938203","https://openalex.org/W3160002757","https://openalex.org/W3161249008","https://openalex.org/W3199159656","https://openalex.org/W3199627414","https://openalex.org/W4409138570"],"related_works":["https://openalex.org/W2156140706","https://openalex.org/W2187310579","https://openalex.org/W2101752691","https://openalex.org/W1517932751","https://openalex.org/W3172619790","https://openalex.org/W4280598225","https://openalex.org/W1545660605","https://openalex.org/W2148726065","https://openalex.org/W2401586919","https://openalex.org/W2035456572"],"abstract_inverted_index":{"Abstract":[0],"We":[1,99],"show":[2,101],"that":[3,84],"the":[4,24,50,91,102,108,111],"existence":[5],"of":[6,26,34,53,71,93,104,110],"a":[7,87],"first-order":[8,97,115],"formula":[9],"separating":[10],"two":[11],"monadic":[12],"second":[13],"order":[14],"formulas":[15],"over":[16],"countable":[17,118],"ordinal":[18,64,82,119],"words":[19],"is":[20],"decidable.":[21],"This":[22],"extends":[23],"work":[25],"Henckell":[27],"and":[28,33,36,107],"Almeida":[29],"on":[30,38,117],"finite":[31],"words,":[32],"Place":[35],"Zeitoun":[37],"$$\\omega":[39,56,74],"$$":[40,57,75],"<mml:math":[41,58,76],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[42,59,77],"<mml:mi>\u03c9</mml:mi>":[43,60,78],"</mml:math>":[44,61,79],"-words.":[45],"For":[46],"this,":[47],"we":[48],"develop":[49],"algebraic":[51],"concept":[52],"monoid":[54],"(resp.":[55,73],"-semigroup,":[62,80],"resp.":[63,81],"monoid)":[65,83],"with":[66],"aperiodic":[67],"merge,":[68],"an":[69],"extension":[70],"monoids":[72],"explicitly":[85],"includes":[86],"new":[88],"operation":[89],"capturing":[90],"loss":[92],"precision":[94],"induced":[95],"by":[96],"indistinguishability.":[98],"also":[100],"computability":[103],"FO-pointlike":[105],"sets,":[106],"decidability":[109],"covering":[112],"problem":[113],"for":[114],"logic":[116],"words.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}