{"id":"https://openalex.org/W2970920732","doi":"https://doi.org/10.1007/978-981-15-0105-0_5","title":"An Improved Proof of the Closure Under Homomorphic Inverse of FCFL Valued in Lattice-Ordered Monoids","display_name":"An Improved Proof of the Closure Under Homomorphic Inverse of FCFL Valued in Lattice-Ordered Monoids","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2970920732","doi":"https://doi.org/10.1007/978-981-15-0105-0_5","mag":"2970920732"},"language":"en","primary_location":{"id":"doi:10.1007/978-981-15-0105-0_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-981-15-0105-0_5","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5042308134","display_name":"Haihui Wang","orcid":"https://orcid.org/0000-0001-6345-0349"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haihui Wang","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061191379","display_name":"Luyao Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luyao Zhao","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100766685","display_name":"Ping Li","orcid":"https://orcid.org/0000-0001-5548-3220"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Li","raw_affiliation_strings":["College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an, 710062, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"64","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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/T11727","display_name":"Advanced Algebra and Logic","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/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9969000220298767,"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/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.7574106454849243},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6835339665412903},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.616449773311615},{"id":"https://openalex.org/keywords/deterministic-context-free-grammar","display_name":"Deterministic context-free grammar","score":0.6035610437393188},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6018548011779785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.548976480960846},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5430116653442383},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4933113157749176},{"id":"https://openalex.org/keywords/pushdown-automaton","display_name":"Pushdown automaton","score":0.46879085898399353},{"id":"https://openalex.org/keywords/inverse-semigroup","display_name":"Inverse semigroup","score":0.46712571382522583},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.43173930048942566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37767112255096436},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36023998260498047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35935360193252563},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33528709411621094},{"id":"https://openalex.org/keywords/context-free-grammar","display_name":"Context-free grammar","score":0.2494770884513855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19914138317108154},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.13660264015197754},{"id":"https://openalex.org/keywords/tree-adjoining-grammar","display_name":"Tree-adjoining grammar","score":0.13011151552200317},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.10915794968605042},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09119167923927307},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07206350564956665}],"concepts":[{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.7574106454849243},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6835339665412903},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.616449773311615},{"id":"https://openalex.org/C177638518","wikidata":"https://www.wikidata.org/wiki/Q3435975","display_name":"Deterministic context-free grammar","level":5,"score":0.6035610437393188},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6018548011779785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.548976480960846},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5430116653442383},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4933113157749176},{"id":"https://openalex.org/C77944639","wikidata":"https://www.wikidata.org/wiki/Q751443","display_name":"Pushdown automaton","level":3,"score":0.46879085898399353},{"id":"https://openalex.org/C2778508345","wikidata":"https://www.wikidata.org/wiki/Q3022118","display_name":"Inverse semigroup","level":3,"score":0.46712571382522583},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.43173930048942566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37767112255096436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36023998260498047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35935360193252563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33528709411621094},{"id":"https://openalex.org/C97212296","wikidata":"https://www.wikidata.org/wiki/Q338047","display_name":"Context-free grammar","level":3,"score":0.2494770884513855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19914138317108154},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.13660264015197754},{"id":"https://openalex.org/C134083981","wikidata":"https://www.wikidata.org/wiki/Q1754022","display_name":"Tree-adjoining grammar","level":4,"score":0.13011151552200317},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.10915794968605042},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09119167923927307},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07206350564956665},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-981-15-0105-0_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-981-15-0105-0_5","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7599999904632568,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W140128488","https://openalex.org/W1545838455","https://openalex.org/W1963807419","https://openalex.org/W1975037151","https://openalex.org/W1982581840","https://openalex.org/W1999673461","https://openalex.org/W2003892275","https://openalex.org/W2004213375","https://openalex.org/W2015539567","https://openalex.org/W2019964946","https://openalex.org/W2032687145","https://openalex.org/W2034940218","https://openalex.org/W2038701822","https://openalex.org/W2043791541","https://openalex.org/W2052520782","https://openalex.org/W2060640081","https://openalex.org/W2062342426","https://openalex.org/W2069701691","https://openalex.org/W2107466240","https://openalex.org/W2111568603","https://openalex.org/W2136244988","https://openalex.org/W2890071412","https://openalex.org/W3150642158","https://openalex.org/W4213325304","https://openalex.org/W4254759562"],"related_works":["https://openalex.org/W1991406344","https://openalex.org/W2012479020","https://openalex.org/W1972232894","https://openalex.org/W2177744885","https://openalex.org/W2074593591","https://openalex.org/W392685101","https://openalex.org/W2116448069","https://openalex.org/W2426482043","https://openalex.org/W2067895928","https://openalex.org/W2373090421"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
