{"id":"https://openalex.org/W1968584500","doi":"https://doi.org/10.2307/2273826","title":"Polynomial size proofs of the propositional pigeonhole principle","display_name":"Polynomial size proofs of the propositional pigeonhole principle","publication_year":1987,"publication_date":"1987-12-01","ids":{"openalex":"https://openalex.org/W1968584500","doi":"https://doi.org/10.2307/2273826","mag":"1968584500"},"language":"en","primary_location":{"id":"doi:10.2307/2273826","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273826","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5103600441","display_name":"Samuel R. Buss","orcid":null},"institutions":[{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samuel R. Buss","raw_affiliation_strings":["Mathematical Sciences Research Institute, Berkeley, California 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, California 94720","institution_ids":["https://openalex.org/I73544541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103600441"],"corresponding_institution_ids":["https://openalex.org/I73544541"],"apc_list":null,"apc_paid":null,"fwci":2.7987,"has_fulltext":false,"cited_by_count":194,"citation_normalized_percentile":{"value":0.91296164,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"52","issue":"4","first_page":"916","last_page":"927"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T10258","display_name":"Philosophy and Theoretical Science","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9909881949424744},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.814201295375824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7058587074279785},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.6417491436004639},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.5305047035217285},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.49401694536209106},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.4769555330276489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4449978768825531},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.4366884231567383},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4334256649017334},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3338410258293152},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21179407835006714},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.08267414569854736},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.05440482497215271},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05190661549568176}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9909881949424744},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.814201295375824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7058587074279785},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.6417491436004639},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.5305047035217285},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.49401694536209106},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.4769555330276489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4449978768825531},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.4366884231567383},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4334256649017334},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3338410258293152},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21179407835006714},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.08267414569854736},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.05440482497215271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05190661549568176},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2273826","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273826","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183742501","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183742501","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.8201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.8201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~sbuss/ResearchWeb/php_PolyFrege/FregePHP_OCR.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1533538517","https://openalex.org/W1572440476","https://openalex.org/W1717854044","https://openalex.org/W1988083342","https://openalex.org/W2014850486","https://openalex.org/W2045924252","https://openalex.org/W2069767473","https://openalex.org/W2098022011","https://openalex.org/W2133527541","https://openalex.org/W3128307576","https://openalex.org/W6654255166","https://openalex.org/W6661988143"],"related_works":["https://openalex.org/W949976107","https://openalex.org/W1987118140","https://openalex.org/W2788816388","https://openalex.org/W2990043628","https://openalex.org/W2951901777","https://openalex.org/W4298267346","https://openalex.org/W3099382357","https://openalex.org/W2063658344","https://openalex.org/W2753667555","https://openalex.org/W2153912760"],"abstract_inverted_index":{"Abstract":[0],"Cook":[1],"and":[2],"Reckhow":[3],"defined":[4],"a":[5,31],"propositional":[6,22],"formulation":[7],"of":[8,20,25,33,38,58],"the":[9],"pigeonhole":[10,23],"principle.":[11],"This":[12,28],"paper":[13],"shows":[14],"that":[15,41],"there":[16],"are":[17],"Frege":[18,42],"proofs":[19],"this":[21],"principle":[24],"polynomial":[26],"size.":[27],"together":[29],"with":[30],"result":[32],"Haken":[34],"gives":[35],"another":[36],"proof":[37],"Urquhart's":[39],"theorem":[40],"systems":[43],"have":[44],"an":[45],"exponential":[46],"speedup":[47],"over":[48],"resolution.":[49],"We":[50],"also":[51],"discuss":[52],"connections":[53],"to":[54],"provability":[55],"in":[56],"theories":[57],"bounded":[59],"arithmetic.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":31},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}