{"id":"https://openalex.org/W2883807093","doi":"https://doi.org/10.1007/978-3-319-96142-2_18","title":"The Proof Complexity of SMT Solvers","display_name":"The Proof Complexity of SMT Solvers","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2883807093","doi":"https://doi.org/10.1007/978-3-319-96142-2_18","mag":"2883807093"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-96142-2_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-96142-2_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/978-3-319-96142-2_18","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021914150","display_name":"Robert Robere","orcid":"https://orcid.org/0000-0002-6065-6023"},"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":true,"raw_author_name":"Robert Robere","raw_affiliation_strings":["University of Toronto, Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003773985","display_name":"Antonina Kolokolova","orcid":null},"institutions":[{"id":"https://openalex.org/I130438778","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03","country_code":"CA","type":"education","lineage":["https://openalex.org/I130438778"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Antonina Kolokolova","raw_affiliation_strings":["Memorial University of Newfoundland, St. John\u2019s, Canada","Memorial University of Newfoundland, St. John's, Canada"],"affiliations":[{"raw_affiliation_string":"Memorial University of Newfoundland, St. John\u2019s, Canada","institution_ids":["https://openalex.org/I130438778"]},{"raw_affiliation_string":"Memorial University of Newfoundland, St. John's, Canada","institution_ids":["https://openalex.org/I130438778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052292970","display_name":"Vijay Ganesh","orcid":"https://orcid.org/0000-0002-6029-2047"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vijay Ganesh","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021914150"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.36,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.8455592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"275","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10142","display_name":"Formal Methods in Verification","score":0.9993000030517578,"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":0.9972000122070312,"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/dpll-algorithm","display_name":"DPLL algorithm","score":0.8157873153686523},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.6094934940338135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5923465490341187},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5672484636306763},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.561012327671051},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5306113362312317},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.49273064732551575},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.4806286692619324},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.47525784373283386},{"id":"https://openalex.org/keywords/branching","display_name":"Branching (polymer chemistry)","score":0.4748119115829468},{"id":"https://openalex.org/keywords/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.47442784905433655},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4734449088573456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43782398104667664},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32269585132598877},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.18467804789543152},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16322636604309082}],"concepts":[{"id":"https://openalex.org/C143936061","wikidata":"https://www.wikidata.org/wiki/Q2030088","display_name":"DPLL algorithm","level":4,"score":0.8157873153686523},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.6094934940338135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5923465490341187},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5672484636306763},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.561012327671051},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5306113362312317},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.49273064732551575},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.4806286692619324},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.47525784373283386},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.4748119115829468},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.47442784905433655},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4734449088573456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43782398104667664},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32269585132598877},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.18467804789543152},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16322636604309082},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C12707504","wikidata":"https://www.wikidata.org/wiki/Q52637","display_name":"Phase-locked loop","level":3,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134652429","wikidata":"https://www.wikidata.org/wiki/Q1052698","display_name":"Jitter","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-96142-2_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-96142-2_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-319-96142-2_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-319-96142-2_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W92576581","https://openalex.org/W112858668","https://openalex.org/W1489527380","https://openalex.org/W1515598460","https://openalex.org/W1982672583","https://openalex.org/W1988083342","https://openalex.org/W2000346568","https://openalex.org/W2022846948","https://openalex.org/W2078608416","https://openalex.org/W2121015471","https://openalex.org/W2129487583","https://openalex.org/W2131455536","https://openalex.org/W2160543001","https://openalex.org/W2171790376","https://openalex.org/W2490907619","https://openalex.org/W2502118804","https://openalex.org/W2604459184","https://openalex.org/W3103546459"],"related_works":["https://openalex.org/W2407696767","https://openalex.org/W106113177","https://openalex.org/W2132634139","https://openalex.org/W2005599008","https://openalex.org/W2590445006","https://openalex.org/W2142612879","https://openalex.org/W39832950","https://openalex.org/W3175751884","https://openalex.org/W860315492","https://openalex.org/W2883807093"],"abstract_inverted_index":{"The":[0],"resolution":[1,42,54],"proof":[2,28,176],"system":[3,127],"has":[4],"been":[5],"enormously":[6],"helpful":[7],"in":[8,210],"deepening":[9],"our":[10],"understanding":[11],"of":[12,24,31,41,49,68,97,107,115,144,217,226],"conflict-driven":[13],"clause-learning":[14,84],"(":[15],"$$\\mathsf":[16,56,74,99,124,146,153],"{CDCL}$$":[17,57,75],")":[18],"SAT":[19,203],"solvers.":[20],"In":[21],"the":[22,50,61,66,112,123,142,174,192,206,211],"interest":[23],"providing":[25],"a":[26,39,94],"similar":[27],"complexity-theoretic":[29],"analysis":[30],"satisfiability":[32],"modulo":[33],"theories":[34],"(SMT)":[35],"solvers,":[36],"we":[37,150,189],"introduce":[38],"generalization":[40],"called":[43],"Res(T).":[44],"We":[45,91,110],"show":[46,121,151],"that":[47,73,122,152,197],"many":[48],"known":[51],"results":[52],"comparing":[53],"and":[55,70,81,120,138,169],"solvers":[58,76,104],"lift":[59],"to":[60,130,181,202],"SMT":[62,103,158],"setting,":[63],"such":[64],"as":[65,205],"result":[67],"Pipatsrisawat":[69],"Darwiche":[71],"showing":[72],"with":[77,117,160],"\u201cperfect\u201d":[78],"non-deterministic":[79],"branching":[80],"an":[82,132,215,224],"asserting":[83],"scheme":[85],"can":[86,172],"polynomially":[87],"simulate":[88,131,173],"general":[89],"resolution.":[90,187],"also":[92],"describe":[93],"stronger":[95],"version":[96],"Res(T),":[98],"{Res}^*$$":[100],"(T),":[101],"capturing":[102],"allowing":[105],"introduction":[106,167],"new":[108,165],"literals.":[109],"analyze":[111],"theory":[113],"EUF":[114,201],"equality":[116],"uninterpreted":[118],"functions,":[119],"{Res}^*(\\mathrm":[125,154],"{EUF})$$":[126,155],"is":[128,179],"able":[129],"earlier":[133],"calculus":[134],"introduced":[135],"by":[136],"Bj\u00f8rner":[137],"de":[139],"Moura":[140],"for":[141],"purpose":[143],"analyzing":[145],"{DPLL}$$":[147],"(EUF).":[148],"Further,":[149],"(and":[156],"thus":[157],"algorithms":[159],"clause":[161],"learning":[162],"over":[163],"EUF,":[164],"literal":[166],"rules":[168],"perfect":[170],"branching)":[171],"Frege":[175],"system,":[177],"which":[178],"well-known":[180],"be":[182],"far":[183],"more":[184],"powerful":[185],"than":[186],"Finally,":[188],"prove":[190],"under":[191],"Exponential":[193],"Time":[194],"Hypothesis":[195],"(ETH)":[196],"any":[198],"reduction":[199],"from":[200,223],"(such":[204],"Ackermann":[207],"reduction)":[208],"must,":[209],"worst":[212],"case,":[213],"produce":[214],"instance":[216,225],"size":[218,227],"$$\\varOmega":[219],"(n":[220],"\\log":[221],"n)$$":[222],"n.":[228]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}