{"id":"https://openalex.org/W1494967481","doi":"https://doi.org/10.1007/3-540-51498-8_13","title":"On product hierarchies of automata","display_name":"On product hierarchies of automata","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W1494967481","doi":"https://doi.org/10.1007/3-540-51498-8_13","mag":"1494967481"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-51498-8_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51498-8_13","pdf_url":null,"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":null,"license_id":null,"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":["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/A5078800242","display_name":"P. D\u00f6m\u00f6si","orcid":null},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"P. D\u00f6m\u00f6si","raw_affiliation_strings":["Dept. of Mathematics, L. Kossuth University, Egyetem t\u00e9r 1., 4010, Debrecen, Hungary"],"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, L. Kossuth University, Egyetem t\u00e9r 1., 4010, Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017293831","display_name":"Zolt\u00e1n \u00c9sik","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Z. \u00c9sik","raw_affiliation_strings":["Bolyai Institute, A. J\u00f3zsef University, Aradi v. tere 1., 6720, Szeged, Hungary","Institute for Informatics, Technical University, M\u00fcnchen, Arcisstr. 21, D - 8000, M\u00fcnchen 2, FRG"],"affiliations":[{"raw_affiliation_string":"Bolyai Institute, A. J\u00f3zsef University, Aradi v. tere 1., 6720, Szeged, Hungary","institution_ids":[]},{"raw_affiliation_string":"Institute for Informatics, Technical University, M\u00fcnchen, Arcisstr. 21, D - 8000, M\u00fcnchen 2, FRG","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025435398","display_name":"Bal\u00e1zs Imreh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Imreh","raw_affiliation_strings":["Bolyai Institute, A. J\u00f3zsef University, Aradi v. tere 1., 6720, Szeged, Hungary"],"affiliations":[{"raw_affiliation_string":"Bolyai Institute, A. J\u00f3zsef University, Aradi v. tere 1., 6720, Szeged, Hungary","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078800242"],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"137","last_page":"144"},"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":0.9983000159263611,"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":0.996999979019165,"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/product","display_name":"Product (mathematics)","score":0.7350403070449829},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.7281600832939148},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.6909748315811157},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6445277333259583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.541883111000061},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5131180882453918},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4644626975059509},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.46148911118507385},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4537442624568939},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.44384101033210754},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4115380644798279},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2661057710647583},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20045939087867737}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.7350403070449829},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.7281600832939148},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.6909748315811157},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6445277333259583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.541883111000061},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5131180882453918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4644626975059509},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.46148911118507385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4537442624568939},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.44384101033210754},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4115380644798279},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2661057710647583},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20045939087867737},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"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/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-51498-8_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51498-8_13","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W83564592","https://openalex.org/W125417455","https://openalex.org/W129775189","https://openalex.org/W203130594","https://openalex.org/W1502820232","https://openalex.org/W1516884046","https://openalex.org/W1605163444","https://openalex.org/W1979895753","https://openalex.org/W2014145003","https://openalex.org/W2059677035","https://openalex.org/W2119777205","https://openalex.org/W2399443219","https://openalex.org/W2468464981","https://openalex.org/W3182360623"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W1963087247","https://openalex.org/W2539930818","https://openalex.org/W2347443236","https://openalex.org/W4205203210","https://openalex.org/W2913232281","https://openalex.org/W2146274131","https://openalex.org/W3012147850","https://openalex.org/W174023083","https://openalex.org/W2184328455"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}