{"id":"https://openalex.org/W2032278512","doi":"https://doi.org/10.1137/0216011","title":"On the Computational Complexity of Algebra on Lattices","display_name":"On the Computational Complexity of Algebra on Lattices","publication_year":1987,"publication_date":"1987-02-01","ids":{"openalex":"https://openalex.org/W2032278512","doi":"https://doi.org/10.1137/0216011","mag":"2032278512"},"language":"en","primary_location":{"id":"doi:10.1137/0216011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216011","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5086835651","display_name":"Harry B. Hunt","orcid":null},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H. B. Hunt, III","raw_affiliation_strings":["State University of New York at Albany Albany"],"affiliations":[{"raw_affiliation_string":"State University of New York at Albany Albany","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009388396","display_name":"Daniel J. Rosenkrantz","orcid":"https://orcid.org/0000-0002-7044-0197"},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. J. Rosenkrantz","raw_affiliation_strings":["State University of New York at Albany Albany"],"affiliations":[{"raw_affiliation_string":"State University of New York at Albany Albany","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075002596","display_name":"Peter A. Bloniarz","orcid":null},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. A. Bloniarz","raw_affiliation_strings":["State University of New York at Albany Albany"],"affiliations":[{"raw_affiliation_string":"State University of New York at Albany Albany","institution_ids":["https://openalex.org/I392282"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086835651"],"corresponding_institution_ids":["https://openalex.org/I392282"],"apc_list":null,"apc_paid":null,"fwci":1.0436,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.74452935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"1","first_page":"129","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.7307318449020386},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.6840438842773438},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6555039882659912},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.5981742143630981},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5931605696678162},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5761836171150208},{"id":"https://openalex.org/keywords/congruence-lattice-problem","display_name":"Congruence lattice problem","score":0.5198657512664795},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4779541492462158},{"id":"https://openalex.org/keywords/map-of-lattices","display_name":"Map of lattices","score":0.4747900366783142},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.473202645778656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4647113084793091},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.46255603432655334},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.460062175989151},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28405383229255676},{"id":"https://openalex.org/keywords/reciprocal-lattice","display_name":"Reciprocal lattice","score":0.15487387776374817},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11197784543037415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10978192090988159},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08779513835906982},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.06947621703147888}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7307318449020386},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.6840438842773438},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6555039882659912},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.5981742143630981},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5931605696678162},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5761836171150208},{"id":"https://openalex.org/C84540187","wikidata":"https://www.wikidata.org/wiki/Q5160997","display_name":"Congruence lattice problem","level":4,"score":0.5198657512664795},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4779541492462158},{"id":"https://openalex.org/C128379363","wikidata":"https://www.wikidata.org/wiki/Q6753757","display_name":"Map of lattices","level":4,"score":0.4747900366783142},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.473202645778656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4647113084793091},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.46255603432655334},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.460062175989151},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28405383229255676},{"id":"https://openalex.org/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.15487387776374817},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11197784543037415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10978192090988159},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08779513835906982},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.06947621703147888},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0216011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216011","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W179752566","https://openalex.org/W1519478560","https://openalex.org/W1598625331","https://openalex.org/W1655990431","https://openalex.org/W1971821372","https://openalex.org/W1977704395","https://openalex.org/W1980857228","https://openalex.org/W1992486652","https://openalex.org/W2017460507","https://openalex.org/W2051516180","https://openalex.org/W2053002696","https://openalex.org/W2319939065","https://openalex.org/W4205529794","https://openalex.org/W4211265583","https://openalex.org/W4245267086"],"related_works":["https://openalex.org/W2963428356","https://openalex.org/W2112873942","https://openalex.org/W4225006771","https://openalex.org/W2045087226","https://openalex.org/W1969507306","https://openalex.org/W2288656848","https://openalex.org/W2049791550","https://openalex.org/W2026041408","https://openalex.org/W3170523711","https://openalex.org/W2367069403"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,106,113,157,175],"computational":[3],"complexity":[4],"of":[5,177],"equivalence":[6,39,114],"and":[7,20,78,115,129,137,161,182],"minimization":[8,117,159,165],"problems":[9,118,166],"for":[10,44,125,138,167,179],"expressions":[11,46,133,140,168,180],"on":[12,30,47,86,134,141,169,184],"many":[13],"different":[14],"lattices":[15],"including":[16],"each":[17,21],"finite":[18,60],"lattice":[19,32,49,63,73,136,144],"distributive":[22,62],"lattice.":[23,155],"A":[24],"general":[25],"efficient":[26],"expressibility":[27],"condition":[28,57,68,76,95],"C":[29,77],"a":[31,72,83,154],"is":[33,41,64,82],"presented":[34],"such":[35],"that":[36,55],"1.":[37],"The":[38],"problem":[40,160,176],"co$NP$":[42],"hard":[43,173],"constant-free":[45,139],"any":[48,135,142],"with":[50,145],"at":[51,146],"least":[52,147],"two":[53],"elements":[54],"satisfies":[56,75,94],"C.":[58,69,96],"Each":[59],"or":[61],"shown":[65],"to":[66,111],"satisfy":[67],"Moreover,":[70],"if":[71,186],"$\\mathcal{L}$":[74,152,170],"$":[79,81],"\\equiv":[80,91],"congruence":[84],"relation":[85],"$\\mathcal{L}$,":[87,185],"then":[88],"${\\mathcal{L}":[89],"/":[90],"}$":[92],"also":[93,101],"Several":[97],"additional":[98],"results":[99,104],"are":[100,119,171],"presented.":[102],"These":[103],"include":[105],"following:":[107],"2.":[108],"In":[109],"contrast":[110],"1,":[112],"operator":[116,158,164],"solvable":[120],"deterministically":[121],"in":[122],"polynomial":[123],"time":[124],"disjunctive":[126],"normal":[127,131],"form":[128,132],"conjunctive":[130],"free":[143],"three":[148],"generators:":[149],"3.":[150],"Let":[151],"be":[153],"Then,":[156],"various":[162],"approximate":[163],"as":[172,174],"determining,":[178],"F":[181],"G":[183],"$F":[187],"\\leqq":[188],"G$.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}