{"id":"https://openalex.org/W7140165523","doi":"https://doi.org/10.48550/arxiv.2603.21353","title":"Classification of Non-redundancy of Boolean Predicates of Arity 4","display_name":"Classification of Non-redundancy of Boolean Predicates of Arity 4","publication_year":2026,"publication_date":"2026-03-22","ids":{"openalex":"https://openalex.org/W7140165523","doi":"https://doi.org/10.48550/arxiv.2603.21353"},"language":"en","primary_location":{"id":"pmh:doi:10.4230/lipics.cp.2026.8","is_oa":true,"landing_page_url":"https://github.com/jbrakensiek/Arity-4-NRD","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"ConferencePaper"},"type":"conference-paper","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://github.com/jbrakensiek/Arity-4-NRD","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Brakensiek, Joshua","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brakensiek, Joshua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Guruswami, Venkatesan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guruswami, Venkatesan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Putterman, Aaron","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Putterman, Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32594818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.3515999913215637,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.3515999913215637,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.22679999470710754,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.06129999831318855,"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/arity","display_name":"Arity","score":0.9739000201225281},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.6676999926567078},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6554999947547913},{"id":"https://openalex.org/keywords/boolean-domain","display_name":"Boolean domain","score":0.6281999945640564},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.45840001106262207},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.44350001215934753},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.4140999913215637},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.41019999980926514},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.40389999747276306},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.3707999885082245}],"concepts":[{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.9739000201225281},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.6676999926567078},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6554999947547913},{"id":"https://openalex.org/C4926405","wikidata":"https://www.wikidata.org/wiki/Q3269980","display_name":"Boolean domain","level":5,"score":0.6281999945640564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6273000240325928},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5218999981880188},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5027999877929688},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.44350001215934753},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.4140999913215637},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.41019999980926514},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32749998569488525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3244999945163727},{"id":"https://openalex.org/C29230964","wikidata":"https://www.wikidata.org/wiki/Q5164376","display_name":"Constraint learning","level":5,"score":0.3224000036716461},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.31540000438690186},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31049999594688416},{"id":"https://openalex.org/C132180345","wikidata":"https://www.wikidata.org/wiki/Q5156628","display_name":"Complexity of constraint satisfaction","level":5,"score":0.3012000024318695},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C73314972","wikidata":"https://www.wikidata.org/wiki/Q10531432","display_name":"Predicate variable","level":5,"score":0.2937000095844269},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.27869999408721924},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.2752000093460083},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C2778975207","wikidata":"https://www.wikidata.org/wiki/Q7078836","display_name":"Of the form","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.4230/lipics.cp.2026.8","is_oa":true,"landing_page_url":"https://github.com/jbrakensiek/Arity-4-NRD","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"ConferencePaper"},{"id":"doi:10.48550/arxiv.2603.21353","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21353","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.4230/lipics.cp.2026.8","is_oa":true,"landing_page_url":"https://github.com/jbrakensiek/Arity-4-NRD","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Given":[0],"a":[1,80],"constraint":[2],"satisfaction":[3],"problem":[4],"(CSP)":[5],"predicate":[6,139],"$P":[7],"\\subseteq":[8],"D^r$,":[9],"the":[10,27,69,84,89,110,124,132,136],"non-redundancy":[11,141],"(NRD)":[12],"of":[13,26,41,50,83,95,107],"$P$":[14],"is":[15,30,46],"maximum-sized":[16],"instance":[17],"on":[18],"$n$":[19],"variables":[20],"such":[21],"that":[22,37],"for":[23,43],"every":[24],"clause":[25],"instance,":[28],"there":[29],"an":[31,47,100,128],"assignment":[32],"which":[33,52,103],"satisfies":[34],"all":[35],"but":[36],"clause.":[38],"The":[39],"study":[40],"NRD":[42],"various":[44],"CSPs":[45],"active":[48],"area":[49],"research":[51],"combines":[53],"ideas":[54],"from":[55],"extremal":[56,119],"combinatorics,":[57],"logic,":[58],"lattice":[59],"theory,":[60],"and":[61,72],"other":[62],"techniques.":[63],"Complete":[64],"classifications":[65],"are":[66,143],"known":[67],"in":[68],"cases":[70],"$r=2$":[71],"$(|D|=2,":[73,86],"r=3)$.":[74],"In":[75],"this":[76],"paper,":[77],"we":[78,98,113,134],"give":[79],"near-complete":[81],"classification":[82],"case":[85],"r=4)$.":[87],"Of":[88,109],"400":[90],"distinct":[91],"non-trivial":[92],"Boolean":[93,138],"predicates":[94],"arity":[96],"4,":[97],"implement":[99],"algorithmic":[101],"procedure":[102],"perfectly":[104],"classifies":[105],"397":[106],"them.":[108],"remaining":[111],"three,":[112],"solve":[114],"two":[115],"by":[116],"reducing":[117],"to":[118],"combinatorics":[120],"problems":[121],"--":[122],"leaving":[123],"last":[125],"one":[126],"as":[127],"open":[129],"question.":[130],"Along":[131],"way,":[133],"identify":[135],"first":[137],"whose":[140],"asymptotics":[142],"non-polynomial.":[144]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2026-03-25T00:00:00"}
