{"id":"https://openalex.org/W2133652713","doi":"https://doi.org/10.1007/bfb0012845","title":"Unification in a combination of arbitrary disjoint equational theories","display_name":"Unification in a combination of arbitrary disjoint equational theories","publication_year":2005,"publication_date":"2005-11-23","ids":{"openalex":"https://openalex.org/W2133652713","doi":"https://doi.org/10.1007/bfb0012845","mag":"2133652713"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0012845","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012845","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":"conference-paper","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.22028/D291-40148","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016539119","display_name":"Manfred Schmidt-Schau\u00df","orcid":"https://orcid.org/0000-0001-8809-7385"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Manfred Schmidt-Schau\u00df","raw_affiliation_strings":["Fachbereich Informatik, Universit\u00e4t Kaiserslautern, Postfach 3049, West Germany","Universit\u00e4t Kaiserslautern"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Informatik, Universit\u00e4t Kaiserslautern, Postfach 3049, West Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Universit\u00e4t Kaiserslautern","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016539119"],"corresponding_institution_ids":["https://openalex.org/I153267046"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.24517382,"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":"378","last_page":"396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","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/T10126","display_name":"Logic, programming, and type systems","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":0.9925000071525574,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9900000095367432,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.9195187091827393},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.808107852935791},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6136350035667419},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5999311208724976},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.49826931953430176},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.47600993514060974},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42614200711250305},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.41845065355300903},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4024308919906616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.245977520942688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1688741147518158}],"concepts":[{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.9195187091827393},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.808107852935791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6136350035667419},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5999311208724976},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.49826931953430176},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.47600993514060974},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42614200711250305},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.41845065355300903},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4024308919906616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.245977520942688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1688741147518158},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bfb0012845","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012845","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"},{"id":"pmh:oai:publikationen.sulb.uni-saarland.de:20.500.11880/36225","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22028/D291-40148","pdf_url":null,"source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:workingPaper"},{"id":"doi:10.22028/d291-40148","is_oa":true,"landing_page_url":"https://doi.org/10.22028/d291-40148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Collection"}],"best_oa_location":{"id":"pmh:oai:publikationen.sulb.uni-saarland.de:20.500.11880/36225","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22028/D291-40148","pdf_url":null,"source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:workingPaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W19055862","https://openalex.org/W60619409","https://openalex.org/W1480465948","https://openalex.org/W1513315908","https://openalex.org/W1523315298","https://openalex.org/W1523684655","https://openalex.org/W1530765221","https://openalex.org/W1593037454","https://openalex.org/W1596011221","https://openalex.org/W1606769915","https://openalex.org/W1753591354","https://openalex.org/W1968229471","https://openalex.org/W1968386045","https://openalex.org/W1979101142","https://openalex.org/W2000095830","https://openalex.org/W2030670832","https://openalex.org/W2033288425","https://openalex.org/W2043918343","https://openalex.org/W2053895806","https://openalex.org/W2056016391","https://openalex.org/W2056637458","https://openalex.org/W2083402938","https://openalex.org/W2100738443","https://openalex.org/W2113722134","https://openalex.org/W2148193906","https://openalex.org/W2776955217","https://openalex.org/W2914314632","https://openalex.org/W3127823229","https://openalex.org/W4213165878","https://openalex.org/W4236632862","https://openalex.org/W4248547811","https://openalex.org/W6600759125","https://openalex.org/W6628668608","https://openalex.org/W6636365093","https://openalex.org/W6642673056","https://openalex.org/W6888796619"],"related_works":["https://openalex.org/W2160250760","https://openalex.org/W1583400373","https://openalex.org/W153224469","https://openalex.org/W1424724424","https://openalex.org/W4286247383","https://openalex.org/W147641928","https://openalex.org/W3191856054","https://openalex.org/W2491308346","https://openalex.org/W2742582826","https://openalex.org/W2566029784"],"abstract_inverted_index":{"The":[0,77,168],"unification":[1,25,163,206,236,261,274,298,316,341,362,366],"problem":[2],"for":[3,119,226,252,380],"terms":[4,89,100,123,141,319],"in":[5,27,36,58,71,124,158,207,241,263,275,300,328,342,350],"a":[6,21,69,149,172,203,208,211,257,264,276,301,307,312,343,381],"disjoint":[7,302],"combination":[8,22,173,209,265,277,303,344],"E":[9,13,28,63,74,245,249,267],"1":[10,246],"+...":[11,247],"+":[12,248],"n":[14,250],"of":[15,23,80,86,174,179,182,186,192,210,266,296,304,317,345,378],"arbitrary":[16],"theories":[17,130,197,349,354],"is":[18,68,132,191,219,256,282],"reduced":[19],"to":[20,39,90,102,108,128,134,144,160,259,291,314],"pure":[24,99],"problems":[26,42,164,237,262],"j":[29,64,75],",":[30],"where":[31,66,322],"free":[32,51,212,216,227,270,279,323,329],"constants":[33],"may":[34,372],"occur":[35],"terms,":[37,321],"and":[38,138,221,332,347,357],"constant":[40,153],"elimination":[41,154],"like:":[43],"find":[44],"all":[45,87,140],"substitutions":[46],"\u03c3":[47],"such":[48,368],"that":[49,171,235,371],"(the":[50],"constant)":[52],"c":[53],"i":[54,254,268],"no":[55],"longer":[56],"occurs":[57],"the":[59,72,81,88,109,117,223,242,283,292,315,337],"term":[60,70],"\u03c3t":[61],"(modulo":[62],"),":[65],"t":[67],"theory":[73,111,137,147],".":[76],"algorithm":[78,118,169],"consists":[79],"following":[82],"basic":[83],"steps:":[84],"First":[85],"be":[91,114,156,233,239],"unified":[92,115],"are":[93,326,355],"transformed":[94],"via":[95],"variable":[96],"abstraction":[97],"into":[98,148],"belonging":[101,107,127,143],"one":[103],"particular":[104,146],"theory.":[105,121,383],"Terms":[106],"same":[110,224],"can":[112,232,238,359],"now":[113],"with":[116,215,269,278],"this":[120,145],"For":[122],"some":[125,136],"multi-equation":[126],"different":[129],"it":[131,231,310],"sufficient":[133],"select":[135],"collapse":[139],"not":[142],"common":[150],"constant.":[151],"Finally":[152],"must":[155],"applied":[157],"order":[159],"solve":[161,260],"cyclic":[162],"like":[165],"\u3008x=f(y),":[166],"y=g(x)\u3009.":[167],"shows":[170],"finitary":[175,199],"unifying":[176],"regular":[177,346],"theories,":[178],"Boolean":[180,213,333],"rings,":[181],"Abelian":[183,228,330],"groups":[184,331],"or":[185],"BNT-theories":[187],"(basic":[188],"narrowing":[189],"terminates)":[190],"unification-type":[193],"finitary,":[194],"since":[195],"these":[196],"have":[198],"constant-elimination":[200],"problems.":[201],"As":[202,306],"special":[204,308,382],"case,":[205],"ring":[214],"function":[217,271,280,324],"symbols":[218,281,325],"decidable":[220],"finitary;":[222],"holds":[225],"groups.":[229],"Remarkably,":[230],"shown":[234],"solved":[240],"general":[243,318],"case":[244,309],"if":[251],"every":[253],"there":[255],"method":[258],"symbols.":[272],"Thus,":[273],"really":[284],"hard":[285],"case.":[286],"This":[287],"paper":[288],"presents":[289],"solutions":[290],"important":[293],"open":[294],"questions":[295],"combining":[297],"algorithms":[299],"theories.":[305],"provides":[311],"solution":[313],"(i.e.":[320],"permitted)":[327],"rings.":[334],"It":[335],"extends":[336],"known":[338],"results":[339],"on":[340],"collapse-free":[348],"two":[351],"aspects:":[352],"Arbitrary":[353],"admissable":[356],"we":[358],"use":[360],"complete":[361,376],"procedures":[363,367],"(including":[364],"universal":[365],"as":[369],"narrowing)":[370],"produce":[373],"an":[374],"infinite":[375],"set":[377],"unifiers":[379]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
