{"id":"https://openalex.org/W2322748670","doi":"https://doi.org/10.1145/2858790","title":"A New Kind of Tradeoffs in Propositional Proof Complexity","display_name":"A New Kind of Tradeoffs in Propositional Proof Complexity","publication_year":2016,"publication_date":"2016-04-07","ids":{"openalex":"https://openalex.org/W2322748670","doi":"https://doi.org/10.1145/2858790","mag":"2322748670"},"language":"en","primary_location":{"id":"doi:10.1145/2858790","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2858790","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","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/A5008113826","display_name":"Alexander Razborov","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexander Razborov","raw_affiliation_strings":["University of Chicago, Departments of Mathematics and Computer Science, Chicago IL, USA"],"affiliations":[{"raw_affiliation_string":"University of Chicago, Departments of Mathematics and Computer Science, Chicago IL, USA","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008113826"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":2.39617418,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.92128943,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"63","issue":"2","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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":0.9976999759674072,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9957000017166138,"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/mathematics","display_name":"Mathematics","score":0.5980804562568665},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5883836150169373},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5755926966667175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.551062285900116},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5468390583992004},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5369493961334229},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.49724701046943665},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4895080327987671},{"id":"https://openalex.org/keywords/contradiction","display_name":"Contradiction","score":0.4712303876876831},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4362873136997223},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.42926162481307983},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.41248995065689087},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.2921419143676758},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28166353702545166},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.12440696358680725},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.11285516619682312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08628466725349426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5980804562568665},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5883836150169373},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5755926966667175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.551062285900116},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5468390583992004},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5369493961334229},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.49724701046943665},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4895080327987671},{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.4712303876876831},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4362873136997223},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.42926162481307983},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.41248995065689087},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.2921419143676758},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28166353702545166},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.12440696358680725},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.11285516619682312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08628466725349426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2858790","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2858790","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G4065927754","display_name":null,"funder_award_id":"# 14-50-00005","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1581386393","https://openalex.org/W1988083342","https://openalex.org/W1994916325","https://openalex.org/W1998375896","https://openalex.org/W2064995417","https://openalex.org/W2074834475","https://openalex.org/W2083975113","https://openalex.org/W2084384424","https://openalex.org/W2092984557","https://openalex.org/W2100738443","https://openalex.org/W2109895531","https://openalex.org/W2122055721","https://openalex.org/W2123346469","https://openalex.org/W2126420408","https://openalex.org/W2129413084","https://openalex.org/W2134253979","https://openalex.org/W2142127354","https://openalex.org/W2160909640","https://openalex.org/W2164319662","https://openalex.org/W2164683439","https://openalex.org/W2166026605","https://openalex.org/W2478857688","https://openalex.org/W2950896461","https://openalex.org/W3037675756","https://openalex.org/W3101351575","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2327230097","https://openalex.org/W2596950579","https://openalex.org/W2384970996","https://openalex.org/W4300342995","https://openalex.org/W2520790414","https://openalex.org/W2008138636","https://openalex.org/W1892325353","https://openalex.org/W2062912795","https://openalex.org/W4301872548","https://openalex.org/W1521370165"],"abstract_inverted_index":{"We":[0],"exhibit":[1],"an":[2,34],"unusually":[3],"strong":[4],"tradeoff":[5],"in":[6,30,36,135,165,186],"propositional":[7],"proof":[8,162],"complexity":[9,50],"that":[10,41,73,88,99,126,130,191],"significantly":[11,200],"deviates":[12],"from":[13],"the":[14,49,52,58,65,139,173,202],"established":[15],"pattern":[16],"of":[17,21,51,61,64,91,103,141,157,196,204],"almost":[18],"all":[19,62],"results":[20,185],"this":[22],"kind.":[23],"Namely,":[24],"restrictions":[25],"on":[26,178],"one":[27],"resource":[28,38],"(width,":[29],"our":[31],"case)":[32],"imply":[33],"increase":[35],"another":[37],"(tree-like":[39],"size)":[40],"is":[42],"exponential":[43,115],"not":[44],"only":[45],"with":[46],"respect":[47],"to":[48,57,137,193],"original":[53],"problem,":[54],"but":[55,97,134],"also":[56],"whole":[59],"class":[60],"problems":[63],"same":[66],"bit":[67],"size.":[68],"More":[69],"specifically,":[70],"we":[71],"show":[72],"for":[74],"any":[75,100],"parameter":[76],"k":[77,79,86,95,110,121],"=":[78],"(":[80,94,118],"n":[81,105,119],"),":[82,96],"there":[83,127],"are":[84],"unsatisfiable":[85],"-CNFs":[87],"possess":[89],"refutations":[90],"width":[92,104],"O":[93],"such":[98,142],"tree-like":[101],"refutation":[102,144],"1":[106],"\u2212":[107],"\u03f5":[108],"/":[109],"must":[111,151],"necessarily":[112,152],"have":[113],"doubly":[114],"size":[116,140],"exp":[117],"\u03a9(":[120],")":[122],").":[123],"This":[124,183],"means":[125],"exist":[128],"contradictions":[129],"allow":[131],"narrow":[132],"refutations,":[133],"order":[136],"keep":[138],"a":[143,147,154,166,187,197],"even":[145],"within":[146],"single":[148],"exponent,":[149],"it":[150],"use":[153],"high":[155],"degree":[156],"parallelism.":[158],"Our":[159],"construction":[160],"and":[161,181],"methods":[163],"combine,":[164],"non-trivial":[167],"way,":[168],"two":[169],"previously":[170],"known":[171],"techniques:":[172],"hardness":[174,188,195],"escalation":[175],"method":[176],"based":[177],"substitution":[179],"formulas":[180],"expansion.":[182],"combination":[184],"compression":[189],"approach":[190],"strives":[192],"preserve":[194],"contradiction":[198],"while":[199],"decreasing":[201],"number":[203],"its":[205],"variables.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}