{"id":"https://openalex.org/W2011321017","doi":"https://doi.org/10.1142/s0218196708004548","title":"WORD EQUATIONS OVER GRAPH PRODUCTS","display_name":"WORD EQUATIONS OVER GRAPH PRODUCTS","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2011321017","doi":"https://doi.org/10.1142/s0218196708004548","mag":"2011321017"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004548","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004548","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/A5054093863","display_name":"Volker Diekert","orcid":"https://orcid.org/0000-0002-5994-3762"},"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":true,"raw_author_name":"VOLKER DIEKERT","raw_affiliation_strings":["Universit\u00e4t Stuttgart, FMI, Universit\u00e4tsstrasse 38, D-70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Stuttgart, FMI, Universit\u00e4tsstrasse 38, D-70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"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/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"MARKUS LOHREY","raw_affiliation_strings":["Universit\u00e4t Leipzig, Institut f\u00fcr Informatik, Johannisgasse 26, D-04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Leipzig, Institut f\u00fcr Informatik, Johannisgasse 26, D-04103 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054093863"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":1.6021,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.83217617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"03","first_page":"493","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10126","display_name":"Logic, programming, and type systems","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9966999888420105,"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/decidability","display_name":"Decidability","score":0.8713529109954834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8456330895423889},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5420492887496948},{"id":"https://openalex.org/keywords/existentialism","display_name":"Existentialism","score":0.5109040141105652},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5011258125305176},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4403945207595825},{"id":"https://openalex.org/keywords/infinite-product","display_name":"Infinite product","score":0.4216320514678955},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41651245951652527}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8713529109954834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8456330895423889},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5420492887496948},{"id":"https://openalex.org/C127882523","wikidata":"https://www.wikidata.org/wiki/Q38066","display_name":"Existentialism","level":2,"score":0.5109040141105652},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5011258125305176},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4403945207595825},{"id":"https://openalex.org/C138888516","wikidata":"https://www.wikidata.org/wiki/Q2266843","display_name":"Infinite product","level":2,"score":0.4216320514678955},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41651245951652527},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196708004548","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004548","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1026721552","https://openalex.org/W1502428252","https://openalex.org/W1505482284","https://openalex.org/W1511526676","https://openalex.org/W1529497146","https://openalex.org/W1545078593","https://openalex.org/W1974069850","https://openalex.org/W1975885036","https://openalex.org/W1977861184","https://openalex.org/W1990939813","https://openalex.org/W1993488464","https://openalex.org/W2000209921","https://openalex.org/W2001280748","https://openalex.org/W2005047182","https://openalex.org/W2009964224","https://openalex.org/W2010175469","https://openalex.org/W2017555772","https://openalex.org/W2022032736","https://openalex.org/W2022598306","https://openalex.org/W2026384981","https://openalex.org/W2027103910","https://openalex.org/W2028685566","https://openalex.org/W2035476945","https://openalex.org/W2039800792","https://openalex.org/W2040480652","https://openalex.org/W2048263388","https://openalex.org/W2060903394","https://openalex.org/W2063022977","https://openalex.org/W2069467851","https://openalex.org/W2071189751","https://openalex.org/W2088024272","https://openalex.org/W2088327549","https://openalex.org/W2089919742","https://openalex.org/W2090997504","https://openalex.org/W2092700841","https://openalex.org/W2163903931","https://openalex.org/W2323378191","https://openalex.org/W2323768040","https://openalex.org/W2491076116","https://openalex.org/W4213009134","https://openalex.org/W4292101339","https://openalex.org/W4302964898"],"related_works":["https://openalex.org/W2385364491","https://openalex.org/W2625646796","https://openalex.org/W3041624257","https://openalex.org/W219899776","https://openalex.org/W4210465737","https://openalex.org/W2356175078","https://openalex.org/W2474767644","https://openalex.org/W2974802953","https://openalex.org/W2158722153","https://openalex.org/W141267447"],"abstract_inverted_index":{"For":[0],"monoids":[1],"that":[2,11,30],"satisfy":[3],"a":[4,35],"weak":[5],"cancellation":[6],"condition,":[7],"it":[8,27],"is":[9,21,28],"shown":[10,29],"the":[12,15,31,44,57,61,71],"decidability":[13],"of":[14,18,34,38,47,60,75],"existential":[16,58],"theory":[17,33],"word":[19],"equations":[20],"preserved":[22],"under":[23],"graph":[24,36],"products.":[25],"Furthermore,":[26],"positive":[32,45],"product":[37],"groups":[39],"can":[40],"be":[41],"reduced":[42],"to":[43,81],"theories":[46,59],"those":[48],"factors,":[49,55],"which":[50],"commute":[51],"with":[52],"all":[53],"other":[54],"and":[56],"remaining":[62],"factors.":[63],"Both":[64],"results":[65],"also":[66],"include":[67],"suitable":[68],"constraints":[69,76],"for":[70],"variables.":[72],"Larger":[73],"classes":[74],"lead":[77],"in":[78],"many":[79],"cases":[80],"undecidability":[82],"results.":[83]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
