{"id":"https://openalex.org/W4389559334","doi":"https://doi.org/10.1007/s00224-023-10154-8","title":"A Closer Look at the Expressive Power of Logics Based on Word Equations","display_name":"A Closer Look at the Expressive Power of Logics Based on Word Equations","publication_year":2023,"publication_date":"2023-12-11","ids":{"openalex":"https://openalex.org/W4389559334","doi":"https://doi.org/10.1007/s00224-023-10154-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-023-10154-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10154-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10154-8.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10154-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033306888","display_name":"Joel D. Day","orcid":"https://orcid.org/0000-0002-3660-7766"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Joel Day","raw_affiliation_strings":["Loughborough University, Loughborough, UK"],"affiliations":[{"raw_affiliation_string":"Loughborough University, Loughborough, UK","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052292970","display_name":"Vijay Ganesh","orcid":"https://orcid.org/0000-0002-6029-2047"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vijay Ganesh","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, N2L, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, N2L, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001776782","display_name":"Nathan Grewal","orcid":"https://orcid.org/0000-0001-7955-5049"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nathan Grewal","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, N2L, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, N2L, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093463916","display_name":"Matthew Konefal","orcid":"https://orcid.org/0009-0003-3346-5517"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew Konefal","raw_affiliation_strings":["Loughborough University, Loughborough, UK"],"affiliations":[{"raw_affiliation_string":"Loughborough University, Loughborough, UK","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006548981","display_name":"Flor\u00edn Manea","orcid":"https://orcid.org/0000-0001-6094-3324"},"institutions":[{"id":"https://openalex.org/I4210116730","display_name":"Universit\u00e4tsmedizin G\u00f6ttingen","ror":"https://ror.org/021ft0n22","country_code":"DE","type":"funder","lineage":["https://openalex.org/I4210116730"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florin Manea","raw_affiliation_strings":["Universit\u00e4t G\u00f6ttingen, G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I4210116730"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5033306888"],"corresponding_institution_ids":["https://openalex.org/I143804889"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.5185,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73133143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"68","issue":"3","first_page":"322","last_page":"379"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10181","display_name":"Natural Language Processing Techniques","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10181","display_name":"Natural Language Processing Techniques","score":0.9990000128746033,"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/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"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/T12479","display_name":"Web Application Security Vulnerabilities","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.6369836330413818},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.5982035398483276},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5975216627120972},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5197727084159851},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4778837263584137},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.4516720473766327},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4189569056034088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3791796863079071},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.373007595539093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3514058589935303},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.3190954923629761},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12090349197387695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08579987287521362}],"concepts":[{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.6369836330413818},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.5982035398483276},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5975216627120972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5197727084159851},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4778837263584137},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.4516720473766327},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4189569056034088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3791796863079071},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.373007595539093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3514058589935303},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.3190954923629761},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12090349197387695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08579987287521362}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00224-023-10154-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10154-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10154-8.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/24659148","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_closer_look_at_the_expressive_power_of_logics_based_on_word_equations/24659148","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/139854","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/139854","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00224-023-10154-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-023-10154-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-023-10154-8.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G1050501348","display_name":null,"funder_award_id":"466789228","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G32528342","display_name":null,"funder_award_id":"466789228.","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389559334.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1017176722","https://openalex.org/W1507052579","https://openalex.org/W1586417893","https://openalex.org/W1993370765","https://openalex.org/W2035476945","https://openalex.org/W2039800792","https://openalex.org/W2053013024","https://openalex.org/W2110318050","https://openalex.org/W2126113681","https://openalex.org/W2131886132","https://openalex.org/W2137370934","https://openalex.org/W2151033407","https://openalex.org/W2166461033","https://openalex.org/W2295723447","https://openalex.org/W2295791966","https://openalex.org/W2482729551","https://openalex.org/W2613188923","https://openalex.org/W2616567161","https://openalex.org/W2776845434","https://openalex.org/W2889237106","https://openalex.org/W2890631112","https://openalex.org/W2897835509","https://openalex.org/W2899573209","https://openalex.org/W2961332145","https://openalex.org/W2962726827","https://openalex.org/W2963054422","https://openalex.org/W2998584877","https://openalex.org/W3033673652","https://openalex.org/W3186328512","https://openalex.org/W3198190303","https://openalex.org/W3211522117","https://openalex.org/W3212912612","https://openalex.org/W3214872226","https://openalex.org/W4205874043","https://openalex.org/W4206405967","https://openalex.org/W4231199984","https://openalex.org/W4233220581","https://openalex.org/W4246691913","https://openalex.org/W4315606097"],"related_works":["https://openalex.org/W2901084331","https://openalex.org/W1526277826","https://openalex.org/W2066136688","https://openalex.org/W2048614185","https://openalex.org/W2912766821","https://openalex.org/W1791602674","https://openalex.org/W1978292968","https://openalex.org/W3099922764","https://openalex.org/W1510002872","https://openalex.org/W2109115134"],"abstract_inverted_index":{"Abstract":[0],"Word":[1],"equations":[2,4,68,145,158,180,228],"are":[3,31,186],"$$\\alpha":[5,18],"\\doteq":[6],"\\beta":[7],"$$":[8,19,26,40],"<mml:math":[9,20,27,41],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[10,21,28,42],"<mml:mrow>":[11],"<mml:mi>\u03b1</mml:mi>":[12,22],"<mml:mo>\u2250</mml:mo>":[13],"<mml:mi>\u03b2</mml:mi>":[14,29],"</mml:mrow>":[15],"</mml:math>":[16,23,30,44],"where":[17],"and":[24,45,83,129,173,194,230],"$$\\beta":[25],"words":[32,75],"consisting":[33],"of":[34,61,72,95,103,113,135,168,171,218],"letters":[35],"from":[36,47,142],"some":[37,231],"alphabet":[38],"$$\\Sigma":[39],"<mml:mi>\u03a3</mml:mi>":[43],"variables":[46],"a":[48,106,114,118,126,133,166,205,215,220],"set":[49,102],"X":[50],".":[51],"Recently,":[52],"there":[53],"has":[54],"been":[55],"substantial":[56],"interest":[57],"in":[58,64,199,238],"the":[59,92,101,169,209,239],"context":[60],"string":[62,86],"solving":[63],"logics":[65,97,140],"combining":[66,143],"word":[67,144,157,179,227],"with":[69,146,159,181],"other":[70,210],"kinds":[71],"constraints":[73,164,185],"on":[74],"such":[76,96],"as":[77,111,165],"(regular)":[78],"language":[79,162,223],"membership":[80,163,184],"(regular":[81],"constraints)":[82],"arithmetic":[84],"over":[85],"lengths":[87],"(length":[88],"constraints).":[89],"We":[90,138,154,176,202,212],"consider":[91,139,156],"expressive":[93],"power":[94],"by":[98,226],"looking":[99],"at":[100],"all":[104,190],"values":[105],"single":[107],"variable":[108],"might":[109],"take":[110],"part":[112],"satisfying":[115],"assignment":[116],"for":[117,235],"given":[119],"formula.":[120],"Hence,":[121],"each":[122,130],"formula-variable":[123],"pair":[124],"defines":[125,132],"formal":[127,136],"language,":[128],"logic":[131],"class":[134],"languages.":[137],"arising":[141],"either":[147],"length":[148,174],"constraints,":[149,151],"regular":[150,172,222,236],"or":[152],"both.":[153],"also":[155,213],"visibly":[160,182],"pushdown":[161,183],"generalisation":[167],"combination":[170],"constraints.":[175],"show":[177],"that":[178],"sufficient":[187],"to":[188],"express":[189],"recursively":[191],"enumerable":[192],"languages":[193,237],"hence":[195],"satisfiability":[196],"is":[197,224],"undecidable":[198],"this":[200],"case.":[201,241],"then":[203],"establish":[204],"strict":[206],"hierarchy":[207],"involving":[208],"combinations.":[211],"provide":[214],"complete":[216],"characterisation":[217],"when":[219],"thin":[221],"expressible":[225],"(alone)":[229],"further":[232],"partial":[233],"results":[234],"general":[240]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
