{"id":"https://openalex.org/W2009964224","doi":"https://doi.org/10.1142/s0218196706003001","title":"LOGICAL ASPECTS OF CAYLEY-GRAPHS: THE MONOID CASE","display_name":"LOGICAL ASPECTS OF CAYLEY-GRAPHS: THE MONOID CASE","publication_year":2006,"publication_date":"2006-04-01","ids":{"openalex":"https://openalex.org/W2009964224","doi":"https://doi.org/10.1142/s0218196706003001","mag":"2009964224"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196706003001","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003001","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5077823013","display_name":"Dietrich Kuske","orcid":null},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"DIETRICH KUSKE","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t Leipzig, D-04109 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t Leipzig, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"MARKUS LOHREY","raw_affiliation_strings":["FMI, Universit\u00e4t Stuttgart, D-70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"FMI, Universit\u00e4t Stuttgart, D-70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077823013"],"corresponding_institution_ids":["https://openalex.org/I926574661"],"apc_list":null,"apc_paid":null,"fwci":2.6963,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89621932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"02","first_page":"307","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9987000226974487,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.8604539632797241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7949801683425903},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.7447277307510376},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.4986748695373535},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49082908034324646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4836648404598236},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.445757120847702},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4347080588340759},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42783766984939575},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4075104594230652},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12799060344696045}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8604539632797241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7949801683425903},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7447277307510376},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.4986748695373535},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49082908034324646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4836648404598236},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.445757120847702},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4347080588340759},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42783766984939575},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4075104594230652},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12799060344696045},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196706003001","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003001","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:lips.informatik.uni-leipzig.de:936","is_oa":false,"landing_page_url":"http://lips.informatik.uni-leipzig.de/?q=node/936","pdf_url":null,"source":{"id":"https://openalex.org/S4377196964","display_name":"Publikation Server (Leipzig University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I926574661","host_organization_name":"Leipzig University","host_organization_lineage":["https://openalex.org/I926574661"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Algebra and Computation 16 (2006), 307-340.","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W67045286","https://openalex.org/W187986157","https://openalex.org/W606453859","https://openalex.org/W1026721552","https://openalex.org/W1487855130","https://openalex.org/W1511526676","https://openalex.org/W1513644114","https://openalex.org/W1517150411","https://openalex.org/W1529497146","https://openalex.org/W1582505610","https://openalex.org/W1593801826","https://openalex.org/W1697762769","https://openalex.org/W1794375813","https://openalex.org/W1870847788","https://openalex.org/W1971416129","https://openalex.org/W1974069850","https://openalex.org/W1975885036","https://openalex.org/W1976522318","https://openalex.org/W1993370765","https://openalex.org/W1993901943","https://openalex.org/W2001280748","https://openalex.org/W2003865102","https://openalex.org/W2006141572","https://openalex.org/W2020079677","https://openalex.org/W2026384981","https://openalex.org/W2062170505","https://openalex.org/W2062792526","https://openalex.org/W2067464091","https://openalex.org/W2071189751","https://openalex.org/W2084488871","https://openalex.org/W2088024272","https://openalex.org/W2088663140","https://openalex.org/W2098676070","https://openalex.org/W2138856440","https://openalex.org/W2148722937","https://openalex.org/W2161792498","https://openalex.org/W2163903931","https://openalex.org/W2296095876","https://openalex.org/W2323378191","https://openalex.org/W2570611167","https://openalex.org/W2594961821","https://openalex.org/W2799061192","https://openalex.org/W2915052804","https://openalex.org/W3037175162","https://openalex.org/W4234400829","https://openalex.org/W4292101339","https://openalex.org/W4302964898"],"related_works":["https://openalex.org/W2331020993","https://openalex.org/W2972379433","https://openalex.org/W4383764068","https://openalex.org/W1481826604","https://openalex.org/W1797057780","https://openalex.org/W1501430220","https://openalex.org/W3187762542","https://openalex.org/W4280598225","https://openalex.org/W4313593731","https://openalex.org/W1511851241"],"abstract_inverted_index":{"Cayley-graphs":[0],"of":[1,9,17,41,47,65,92,109,113],"monoids":[2],"are":[3,97,127],"investigated":[4],"under":[5,31,53,78],"a":[6,24,39,72,114],"logical":[7],"point":[8],"view.":[10],"It":[11,103],"is":[12,29,36,51,60,76,104,116],"shown":[13,61,105],"that":[14,44,62,106],"the":[15,21,45,63,69,90,107,110],"class":[16,64],"monoids,":[18,66],"for":[19,67],"which":[20,68,82],"Cayley-graph":[22,70],"has":[23,71],"decidable":[25,73],"monadic":[26,48],"second-order":[27,49],"theory,":[28,75],"closed":[30,77],"free":[32,85],"products.":[33,88],"This":[34],"result":[35,40],"derived":[37],"from":[38],"Walukiewicz,":[42],"stating":[43],"decidability":[46,108],"theories":[50],"preserved":[52,117],"tree-like":[54,95],"unfoldings.":[55,102,120],"Concerning":[56],"first-order":[57,74,111],"logic,":[58],"it":[59],"arbitrary":[79],"graph":[80],"products,":[81],"generalize":[83],"both,":[84],"and":[86],"direct":[87],"For":[89],"proof":[91],"this":[93],"result,":[94],"unfoldings":[96,126],"generalized":[98],"to":[99],"so-called":[100],"factorized":[101,119,125],"theory":[112],"structure":[115],"by":[118],"Several":[121],"additional":[122],"results":[123],"concerning":[124],"shown.":[128]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}