{"id":"https://openalex.org/W2075146634","doi":"https://doi.org/10.1305/ndjfl/1040046140","title":"Simplified Lower Bounds for Propositional Proofs","display_name":"Simplified Lower Bounds for Propositional Proofs","publication_year":1996,"publication_date":"1996-10-01","ids":{"openalex":"https://openalex.org/W2075146634","doi":"https://doi.org/10.1305/ndjfl/1040046140","mag":"2075146634"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1040046140","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040046140","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-37/issue-4/Simplified-Lower-Bounds-for-Propositional-Proofs/10.1305/ndjfl/1040046140.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-37/issue-4/Simplified-Lower-Bounds-for-Propositional-Proofs/10.1305/ndjfl/1040046140.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070276200","display_name":"Xudong Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xudong Fu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110161787","display_name":"Alasdair Urquhart","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alasdair Urquhart","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":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.20499271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9986000061035156,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9692033529281616},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8860181570053101},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.7259037494659424},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6271735429763794},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5349546670913696},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5231229662895203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4772876799106598},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.464703232049942},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.43297722935676575},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.42928919196128845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27363577485084534},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14352861046791077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05491861701011658},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.04708018898963928}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9692033529281616},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8860181570053101},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.7259037494659424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6271735429763794},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5349546670913696},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5231229662895203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4772876799106598},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.464703232049942},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.43297722935676575},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.42928919196128845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27363577485084534},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14352861046791077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05491861701011658},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.04708018898963928},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1040046140","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040046140","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-37/issue-4/Simplified-Lower-Bounds-for-Propositional-Proofs/10.1305/ndjfl/1040046140.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1040046140","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1040046140","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"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1040046140","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040046140","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-37/issue-4/Simplified-Lower-Bounds-for-Propositional-Proofs/10.1305/ndjfl/1040046140.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310174","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2075146634.pdf","grobid_xml":"https://content.openalex.org/works/W2075146634.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1563012911","https://openalex.org/W2014850486","https://openalex.org/W2017290750","https://openalex.org/W2029390834","https://openalex.org/W2045924252","https://openalex.org/W2082187221","https://openalex.org/W2098022011","https://openalex.org/W2109174551","https://openalex.org/W2126420408","https://openalex.org/W2133527541","https://openalex.org/W2135672707","https://openalex.org/W2167115661","https://openalex.org/W2169713712","https://openalex.org/W2275166338","https://openalex.org/W4245630182"],"related_works":["https://openalex.org/W1662675122","https://openalex.org/W2531336559","https://openalex.org/W4288055874","https://openalex.org/W2135672707","https://openalex.org/W4301376359","https://openalex.org/W2952905372","https://openalex.org/W20075351","https://openalex.org/W2753667555","https://openalex.org/W2153912760","https://openalex.org/W4321153753"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"a":[3],"simplified":[4],"proof":[5,22],"of":[6,14],"the":[7,15,24],"result":[8,38],"that":[9],"bounded":[10],"depth":[11],"propositional":[12],"proofs":[13],"pigeonhole":[16],"principle":[17],"are":[18],"exponentially":[19],"large.":[20],"The":[21],"uses":[23],"new":[25],"techniques":[26],"for":[27,42],"proving":[28],"switching":[29],"lemmas":[30],"developed":[31],"by":[32],"Razborov":[33],"and":[34],"Beame.":[35],"A":[36],"similar":[37],"is":[39],"also":[40],"proved":[41],"some":[43],"examples":[44],"based":[45],"on":[46],"graphs.":[47]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
