{"id":"https://openalex.org/W7168137866","doi":"https://doi.org/10.4230/lipics.cp.2026.8","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":"2026-01-01","ids":{"openalex":"https://openalex.org/W7168137866","doi":"https://doi.org/10.4230/lipics.cp.2026.8"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26641","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.8","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol379-cp2026/LIPIcs.CP.2026.8/LIPIcs.CP.2026.8.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol379-cp2026/LIPIcs.CP.2026.8/LIPIcs.CP.2026.8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028220417","display_name":"Joshua Brakensiek","orcid":"https://orcid.org/0000-0003-4149-7298"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brakensiek, Joshua","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-4149-7298","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068388812","display_name":"Venkatesan Guruswami","orcid":"https://orcid.org/0000-0001-7926-3396"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guruswami, Venkatesan","raw_affiliation_strings":["Simons Institute for the Theory of Computing and the University of California, Berkeley, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7926-3396","affiliations":[{"raw_affiliation_string":"Simons Institute for the Theory of Computing and the University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I4210107338"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091954510","display_name":"Aaron Putterman","orcid":"https://orcid.org/0000-0001-9737-2406"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Putterman, Aaron","raw_affiliation_strings":["School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-9737-2406","affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.83105956,"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":0.42739999294281006,"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":0.42739999294281006,"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":0.149399995803833,"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":0.0860000029206276,"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":0.9721999764442444},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.6653000116348267},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6509000062942505},{"id":"https://openalex.org/keywords/boolean-domain","display_name":"Boolean domain","score":0.6366999745368958},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4580000042915344},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.42730000615119934},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.39649999141693115},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.38769999146461487},{"id":"https://openalex.org/keywords/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.3718000054359436},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.36899998784065247}],"concepts":[{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.9721999764442444},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.6653000116348267},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6509000062942505},{"id":"https://openalex.org/C4926405","wikidata":"https://www.wikidata.org/wiki/Q3269980","display_name":"Boolean domain","level":5,"score":0.6366999745368958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6360999941825867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5462999939918518},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5253000259399414},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.42730000615119934},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.39649999141693115},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.38769999146461487},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.3249000012874603},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.3199000060558319},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.30640000104904175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30480000376701355},{"id":"https://openalex.org/C29230964","wikidata":"https://www.wikidata.org/wiki/Q5164376","display_name":"Constraint learning","level":5,"score":0.30079999566078186},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2962000072002411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.287200003862381},{"id":"https://openalex.org/C132180345","wikidata":"https://www.wikidata.org/wiki/Q5156628","display_name":"Complexity of constraint satisfaction","level":5,"score":0.28130000829696655},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.26840001344680786},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C73314972","wikidata":"https://www.wikidata.org/wiki/Q10531432","display_name":"Predicate variable","level":5,"score":0.2680000066757202},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.26600000262260437},{"id":"https://openalex.org/C2778975207","wikidata":"https://www.wikidata.org/wiki/Q7078836","display_name":"Of the form","level":2,"score":0.26429998874664307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26641","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.8","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol379-cp2026/LIPIcs.CP.2026.8/LIPIcs.CP.2026.8.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"InProceedings"},{"id":"doi:10.4230/lipics.cp.2026.8","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.cp.2026.8","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26641","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.8","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol379-cp2026/LIPIcs.CP.2026.8/LIPIcs.CP.2026.8.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"InProceedings"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3836720563","display_name":"Postdoctoral Fellowship: MSPRF: Bridging Coding Theory and Constraint Satisfaction via Locality","funder_award_id":"2503280","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7587476858","display_name":null,"funder_award_id":"CCF-2211972","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7922950424","display_name":"Collaborative Research: AF: Medium: Polynomial Optimization: Algorithms, Certificates and Applications","funder_award_id":"2211972","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8779882045","display_name":null,"funder_award_id":"DMS-2503280","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7168137866.pdf","grobid_xml":"https://content.openalex.org/works/W7168137866.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Given":[0],"a":[1,88],"constraint":[2],"satisfaction":[3],"problem":[4],"(CSP)":[5],"predicate":[6,151],"P":[7,14],"\u2286":[8],"D^r,":[9],"the":[10,16,28,71,92,101,122,136,144,148],"non-redundancy":[11,153],"(NRD)":[12],"of":[13,27,43,52,91,107,119],"is":[15,31,48],"maximum-sized":[17],"instance":[18],"on":[19],"n":[20],"variables":[21],"such":[22],"that":[23,39],"for":[24,45],"every":[25],"clause":[26],"instance,":[29],"there":[30],"an":[32,49,112,140],"assignment":[33],"which":[34,54,115],"satisfies":[35],"all":[36],"clauses":[37],"but":[38],"one.":[40],"The":[41],"study":[42],"NRD":[44],"various":[46],"CSPs":[47],"active":[50],"area":[51],"research":[53],"combines":[55],"ideas":[56],"from":[57],"extremal":[58,131],"combinatorics,":[59],"logic,":[60],"lattice":[61],"theory,":[62],"and":[63,76],"other":[64],"techniques.":[65],"Complete":[66],"classifications":[67],"are":[68,155],"known":[69],"in":[70],"cases":[72],"r":[73,80,97],"=":[74,78,81,95,98],"2":[75],"(|D|":[77,94],"2,":[79,96],"3).":[82],"In":[83],"this":[84],"paper,":[85],"we":[86,110,125,146],"give":[87],"near-complete":[89],"classification":[90],"case":[93],"4).":[99],"Of":[100,121],"400":[102],"distinct":[103],"non-trivial":[104],"Boolean":[105,150],"predicates":[106],"arity":[108],"4,":[109],"implement":[111],"algorithmic":[113],"procedure":[114],"perfectly":[116],"classifies":[117],"397":[118],"them.":[120],"remaining":[123],"three,":[124],"solve":[126],"two":[127],"by":[128],"reducing":[129],"to":[130],"combinatorics":[132],"problems":[133],"-":[134],"leaving":[135],"last":[137],"one":[138],"as":[139],"open":[141],"question.":[142],"Along":[143],"way,":[145],"identify":[147],"first":[149],"whose":[152],"asymptotics":[154],"non-polynomial.":[156]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2026-07-14T00:00:00"}