{"id":"https://openalex.org/W2950968656","doi":"https://doi.org/10.23638/lmcs-13(3:9)2017","title":"The Algebraic Intersection Type Unification Problem","display_name":"The Algebraic Intersection Type Unification Problem","publication_year":2017,"publication_date":"2017-08-15","ids":{"openalex":"https://openalex.org/W2950968656","doi":"https://doi.org/10.23638/lmcs-13(3:9)2017","mag":"2950968656"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-13(3:9)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:9)2017","pdf_url":"https://lmcs.episciences.org/3858/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/3858/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017299598","display_name":"Andrej Dudenhefner","orcid":"https://orcid.org/0000-0003-1104-444X"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andrej Dudenhefner","raw_affiliation_strings":["Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","Department of Computer Science, Technical University of Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Department of Computer Science, Technical University of Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090514298","display_name":"Moritz Martens","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz Martens","raw_affiliation_strings":["Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","Department of Computer Science, Technical University of Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Department of Computer Science, Technical University of Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081497785","display_name":"Jakob Rehof","orcid":"https://orcid.org/0000-0002-6023-8921"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jakob Rehof","raw_affiliation_strings":["Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","Department of Computer Science, Technical University of Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Technical University of Dortmund , Dortmund , Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Department of Computer Science, Technical University of Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017299598"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":null,"apc_paid":null,"fwci":0.237,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62000078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"Volume 13, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9918000102043152,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9918000102043152,"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/T10142","display_name":"Formal Methods in Verification","score":0.9872000217437744,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/unification","display_name":"Unification","score":0.7071215510368347},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6930432319641113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5376213192939758},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.536548376083374},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.528322160243988},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38792216777801514},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33190786838531494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2539885640144348},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10614442825317383},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09407562017440796},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.08789050579071045},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.048108458518981934},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.03515028953552246}],"concepts":[{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.7071215510368347},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6930432319641113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5376213192939758},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.536548376083374},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.528322160243988},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38792216777801514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33190786838531494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2539885640144348},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10614442825317383},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09407562017440796},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.08789050579071045},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.048108458518981934},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.03515028953552246},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.23638/lmcs-13(3:9)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:9)2017","pdf_url":"https://lmcs.episciences.org/3858/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.05672","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.05672","pdf_url":"https://arxiv.org/pdf/1611.05672","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:f707db9efd1f4096abc5f54281676aaa","is_oa":true,"landing_page_url":"https://doaj.org/article/f707db9efd1f4096abc5f54281676aaa","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 13, Issue 3 (2017)","raw_type":"article"},{"id":"pmh:oai:fraunhofer.de:N-577793","is_oa":true,"landing_page_url":"http://publica.fraunhofer.de/documents/N-577793.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"Fraunhofer ISST","raw_type":"Journal Article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/261149","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/261149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.23638/lmcs-13(3:9)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:9)2017","pdf_url":"https://lmcs.episciences.org/3858/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950968656.pdf","grobid_xml":"https://content.openalex.org/works/W2950968656.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W21463807","https://openalex.org/W49615274","https://openalex.org/W115606789","https://openalex.org/W1479945718","https://openalex.org/W1508807075","https://openalex.org/W1527933453","https://openalex.org/W1576727331","https://openalex.org/W1596346405","https://openalex.org/W1763589622","https://openalex.org/W1880804819","https://openalex.org/W1921642287","https://openalex.org/W1966026637","https://openalex.org/W1970227944","https://openalex.org/W1975341792","https://openalex.org/W1985092102","https://openalex.org/W1991090339","https://openalex.org/W1993695344","https://openalex.org/W2030473999","https://openalex.org/W2049209348","https://openalex.org/W2087381628","https://openalex.org/W2087871591","https://openalex.org/W2099162225","https://openalex.org/W2120254577","https://openalex.org/W2123812977","https://openalex.org/W2132037187","https://openalex.org/W2196653126","https://openalex.org/W2288082802","https://openalex.org/W2398664406","https://openalex.org/W3003891805","https://openalex.org/W4206013133","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2367630557","https://openalex.org/W101666983","https://openalex.org/W2183792531","https://openalex.org/W2595286499","https://openalex.org/W2794344379","https://openalex.org/W2489197555","https://openalex.org/W2471908688","https://openalex.org/W1845283042","https://openalex.org/W3171337446","https://openalex.org/W2884423176"],"abstract_inverted_index":{"The":[0,114],"algebraic":[1,31,103,125],"intersection":[2,20,32,89,104,118],"type":[3,21,33,90,105],"unification":[4,34,106,112],"problem":[5,35,47,107,151,175],"is":[6,24,36,55,95,152],"an":[7,124,128],"important":[8],"component":[9],"in":[10,19,108,165,201],"proof":[11],"search":[12],"related":[13],"to":[14,75,97,143,159,182,196],"several":[15],"natural":[16,154],"decision":[17],"problems":[18],"systems.":[22],"It":[23],"unknown":[25],"and":[26,132,155,170,204],"remains":[27],"open":[28],"whether":[29],"the":[30,40,46,102,109,150,166,174,184,188],"decidable.":[37],"We":[38,100],"give":[39],"first":[41],"nontrivial":[42],"lower":[43,189],"bound":[44,190],"for":[45,88,187,208],"by":[48],"showing":[49],"(our":[50],"main":[51],"result)":[52],"that":[53,62,177],"it":[54,157],"exponential":[56],"time":[57],"hard.":[58],"Furthermore,":[59],"we":[60,82,192],"show":[61],"this":[63],"holds":[64],"even":[65],"under":[66],"rank":[67,77],"1":[68,78],"solutions":[69],"(substitutions":[70],"whose":[71],"codomains":[72],"are":[73,180],"restricted":[74],"contain":[76],"types).":[79],"In":[80],"addition,":[81],"provide":[83],"a":[84,144,161],"fixed-parameter":[85],"intractability":[86],"result":[87],"matching":[91],"(one-sided":[92],"unification),":[93],"which":[94],"known":[96,199],"be":[98,121],"NP-complete.":[99],"place":[101,164],"context":[110],"of":[111,117,168,173],"theory.":[113],"equational":[115],"theory":[116,126,167,203],"types":[119],"can":[120],"presented":[122],"as":[123],"with":[127,138,141],"ACI":[129],"(associative,":[130],"commutative,":[131],"idempotent)":[133],"operator":[134,146],"(intersection":[135],"type)":[136],"combined":[137],"distributivity":[139],"properties":[140],"respect":[142],"second":[145],"(function":[147],"type).":[148],"Although":[149],"algebraically":[153],"interesting,":[156],"appears":[158],"occupy":[160],"hitherto":[162],"unstudied":[163],"unification,":[169],"our":[171],"investigation":[172],"suggests":[176],"new":[178],"methods":[179,207],"required":[181],"understand":[183],"problem.":[185],"Thus,":[186],"proof,":[191],"were":[193],"not":[194],"able":[195],"reduce":[197],"from":[198],"results":[200],"ACI-unification":[202],"use":[205],"game-theoretic":[206],"two-player":[209],"tiling":[210],"games.":[211]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
