{"id":"https://openalex.org/W2102098509","doi":"https://doi.org/10.1109/sfcs.2002.1181982","title":"Bounded-depth Frege lower bounds for weaker pigeonhole principles","display_name":"Bounded-depth Frege lower bounds for weaker pigeonhole principles","publication_year":2003,"publication_date":"2003-06-26","ids":{"openalex":"https://openalex.org/W2102098509","doi":"https://doi.org/10.1109/sfcs.2002.1181982","mag":"2102098509"},"language":"en","primary_location":{"id":"doi:10.1109/sfcs.2002.1181982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2002.1181982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5111441480","display_name":"J. Buresh-Oppenheim","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"J. Buresh-Oppenheim","raw_affiliation_strings":["Computer Science Department, University of Toronto, Toronto, ONT, Canada","Dept. of Comput. Sci., Toronto Univ., Ont., Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Toronto Univ., Ont., Canada","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042076941","display_name":"Paul Beame","orcid":"https://orcid.org/0000-0002-2666-3545"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Beame","raw_affiliation_strings":["Computer Science and Engineering, University of Washington, Seattle, WA, USA","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003318200","display_name":"Toniann Pitassi","orcid":"https://orcid.org/0000-0002-8668-2174"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"T. Pitassi","raw_affiliation_strings":["Computer Science Department, University of Toronto, Toronto, ONT, Canada","University of Toronto"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041545934","display_name":"Ran Raz","orcid":"https://orcid.org/0009-0008-1656-2258"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"R. Raz","raw_affiliation_strings":["Faculty of Math and Computer Science, Weizmann Institute of Science, Rehovot, Israel","Weizmann Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Math and Computer Science, Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077726785","display_name":"Ashish Sabharwal","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Sabharwal","raw_affiliation_strings":["Computer Science and Engineering, University of Washington, Seattle, WA, USA","University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2604,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48778655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":null,"first_page":"583","last_page":"592"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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":0.9945999979972839,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9876000285148621,"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9735503196716309},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.8349615335464478},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7702763080596924},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7516500949859619},{"id":"https://openalex.org/keywords/tautology","display_name":"Tautology (logic)","score":0.7412893772125244},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7174449563026428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6661359071731567},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5360740423202515},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.5029293894767761},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.48132359981536865},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4384087920188904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17963311076164246},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09032014012336731},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.08135327696800232}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9735503196716309},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8349615335464478},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7702763080596924},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7516500949859619},{"id":"https://openalex.org/C166374712","wikidata":"https://www.wikidata.org/wiki/Q209555","display_name":"Tautology (logic)","level":5,"score":0.7412893772125244},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7174449563026428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6661359071731567},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5360740423202515},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.5029293894767761},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.48132359981536865},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4384087920188904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17963311076164246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09032014012336731},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.08135327696800232},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/sfcs.2002.1181982","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2002.1181982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W75109858","https://openalex.org/W157950381","https://openalex.org/W256057417","https://openalex.org/W1514413980","https://openalex.org/W1521859395","https://openalex.org/W1538043890","https://openalex.org/W1563012911","https://openalex.org/W1572440476","https://openalex.org/W1607926272","https://openalex.org/W1968584500","https://openalex.org/W2029390834","https://openalex.org/W2060270693","https://openalex.org/W2062912795","https://openalex.org/W2069767473","https://openalex.org/W2075146634","https://openalex.org/W2089534194","https://openalex.org/W2093396771","https://openalex.org/W2095226356","https://openalex.org/W2102977254","https://openalex.org/W2109174551","https://openalex.org/W2123878503","https://openalex.org/W2124115465","https://openalex.org/W2130847546","https://openalex.org/W2134961930","https://openalex.org/W2143313747","https://openalex.org/W2165293955","https://openalex.org/W2169713712","https://openalex.org/W2170605748","https://openalex.org/W4206555336","https://openalex.org/W4232748410","https://openalex.org/W6603003492","https://openalex.org/W6631315792","https://openalex.org/W6632309504","https://openalex.org/W6634525871"],"related_works":["https://openalex.org/W1998171255","https://openalex.org/W4221036368","https://openalex.org/W4288055874","https://openalex.org/W1662675122","https://openalex.org/W2068071783","https://openalex.org/W2098308941","https://openalex.org/W2531336559","https://openalex.org/W2063658344","https://openalex.org/W2165390183","https://openalex.org/W2159783982"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,45],"quasi-polynomial":[3],"lower":[4,28,51],"bound":[5,29],"on":[6],"the":[7,14,32,61,73],"size":[8],"of":[9,13],"bounded-depth":[10,35,54],"Frege":[11,36,55],"proofs":[12,37],"pigeonhole":[15],"principle":[16],"PHP/sub":[17],"n//sup":[18],"m/":[19],"where":[20],"m":[21],"=":[22],"(1":[23],"+":[24],"1/polylog":[25],"n)n.":[26],"This":[27],"qualitatively":[30],"matches":[31],"known":[33],"quasipolynomial-size":[34],"for":[38,53],"these":[39],"principles.":[40],"Our":[41],"technique,":[42],"which":[43,64],"uses":[44],"switching":[46,66],"lemma":[47,67],"argument":[48],"like":[49],"other":[50],"bounds":[52],"proofs,":[56],"is":[57,68],"novel":[58],"in":[59],"that":[60],"tautology":[62],"to":[63],"this":[65],"applied":[69],"remains":[70],"random":[71],"throughout":[72],"argument.":[74]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}