{"id":"https://openalex.org/W3128482754","doi":"https://doi.org/10.3233/faia200990","title":"Chapter 7. Proof Complexity and SAT Solving","display_name":"Chapter 7. Proof Complexity and SAT Solving","publication_year":2021,"publication_date":"2021-02-02","ids":{"openalex":"https://openalex.org/W3128482754","doi":"https://doi.org/10.3233/faia200990","mag":"3128482754"},"language":"en","primary_location":{"id":"doi:10.3233/faia200990","is_oa":false,"landing_page_url":"https://doi.org/10.3233/faia200990","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","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/A5067079243","display_name":"Sam Buss","orcid":"https://orcid.org/0000-0003-3837-334X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sam Buss","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003633660","display_name":"Jakob Nordstr\u0094\u00f6m","orcid":"https://orcid.org/0000-0002-2700-4285"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Jakob Nordstr\u00f6m","raw_affiliation_strings":["K\u00f8benhavns Universitet, Faculty of Science, Department of Computer Science, Algorithms and Complexity, DK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K\u00f8benhavns Universitet, Faculty of Science, Department of Computer Science, Algorithms and Complexity, DK","institution_ids":["https://openalex.org/I4210099593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7969,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.97762032,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9991999864578247,"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":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.6295528411865234},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5041157007217407},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45780324935913086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40749871730804443},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39337480068206787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3702821135520935},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32200920581817627},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14381325244903564},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.1263280212879181},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11759021878242493}],"concepts":[{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.6295528411865234},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5041157007217407},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45780324935913086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40749871730804443},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39337480068206787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3702821135520935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32200920581817627},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14381325244903564},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.1263280212879181},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11759021878242493},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3233/faia200990","is_oa":false,"landing_page_url":"https://doi.org/10.3233/faia200990","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},{"id":"pmh:oai:lup.lub.lu.se:e5ed752b-55bf-40c9-8818-f18056a8ff4a","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/e5ed752b-55bf-40c9-8818-f18056a8ff4a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/bookPart"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9b99fba0-bf96-4c5d-9730-dcab35822e2b","is_oa":false,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/9b99fba0-bf96-4c5d-9730-dcab35822e2b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Buss , S & Nordstr\u00f6m , J 2021 , Proof Complexity and SAT Solving . in A Biere , M J H Heule , H van Maaren & T Walsh (eds) , Handbook of Satisfiability . 2 edn , IMIA and IOS Press , Frontiers in Artificial Intelligence and Applications , vol. 336 , pp. 233 - 350 . https://doi.org/10.3233/FAIA200990","raw_type":"bookPart"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":83,"referenced_works":["https://openalex.org/W33157876","https://openalex.org/W46203810","https://openalex.org/W64175367","https://openalex.org/W78552530","https://openalex.org/W94961302","https://openalex.org/W139740642","https://openalex.org/W242035403","https://openalex.org/W1505776303","https://openalex.org/W1518031539","https://openalex.org/W1519724636","https://openalex.org/W1541826589","https://openalex.org/W1567053297","https://openalex.org/W1594732291","https://openalex.org/W1966303481","https://openalex.org/W1968584500","https://openalex.org/W1968655942","https://openalex.org/W1974070050","https://openalex.org/W1985854796","https://openalex.org/W1990360244","https://openalex.org/W1999067488","https://openalex.org/W1999069928","https://openalex.org/W2007575279","https://openalex.org/W2012476164","https://openalex.org/W2022540723","https://openalex.org/W2030224590","https://openalex.org/W2035926913","https://openalex.org/W2036265926","https://openalex.org/W2038169576","https://openalex.org/W2040082402","https://openalex.org/W2040813688","https://openalex.org/W2041857712","https://openalex.org/W2045690379","https://openalex.org/W2057361103","https://openalex.org/W2063658344","https://openalex.org/W2067241820","https://openalex.org/W2071347463","https://openalex.org/W2071596701","https://openalex.org/W2074834475","https://openalex.org/W2091961944","https://openalex.org/W2105447726","https://openalex.org/W2108637261","https://openalex.org/W2117427692","https://openalex.org/W2120006490","https://openalex.org/W2122782108","https://openalex.org/W2124685959","https://openalex.org/W2129413084","https://openalex.org/W2132148988","https://openalex.org/W2136687801","https://openalex.org/W2137378957","https://openalex.org/W2142127354","https://openalex.org/W2144512014","https://openalex.org/W2145243417","https://openalex.org/W2146777332","https://openalex.org/W2147442986","https://openalex.org/W2160543001","https://openalex.org/W2163846023","https://openalex.org/W2165390183","https://openalex.org/W2167115661","https://openalex.org/W2170001390","https://openalex.org/W2171790376","https://openalex.org/W2217204207","https://openalex.org/W2282536569","https://openalex.org/W2323554188","https://openalex.org/W2396393208","https://openalex.org/W2499282942","https://openalex.org/W2554686331","https://openalex.org/W2563018125","https://openalex.org/W2773116874","https://openalex.org/W2791949701","https://openalex.org/W2808706008","https://openalex.org/W2809359463","https://openalex.org/W2811168821","https://openalex.org/W2811247337","https://openalex.org/W2905780568","https://openalex.org/W2943545475","https://openalex.org/W2950227315","https://openalex.org/W2954910840","https://openalex.org/W2965705192","https://openalex.org/W2997126574","https://openalex.org/W3004119281","https://openalex.org/W3021939903","https://openalex.org/W3045335116","https://openalex.org/W3083069078"],"related_works":["https://openalex.org/W1618870210","https://openalex.org/W2122055721","https://openalex.org/W2804939161","https://openalex.org/W2400565179","https://openalex.org/W2778491775","https://openalex.org/W2086871557","https://openalex.org/W3013210104","https://openalex.org/W2288678542","https://openalex.org/W2062949469","https://openalex.org/W2074946288"],"abstract_inverted_index":{"This":[0],"chapter":[1],"gives":[2],"an":[3],"overview":[4],"of":[5,48,70],"proof":[6,15,57],"complexity":[7],"and":[8,23,39,59,61],"connections":[9],"to":[10,27,55],"SAT":[11],"solving,":[12,41],"focusing":[13],"on":[14],"systems":[16,64],"such":[17],"as":[18],"resolution,":[19],"Nullstellensatz,":[20],"polynomial":[21],"calculus,":[22],"cutting":[24],"planes":[25],"(corresponding":[26],"conflict-driven":[28],"clause":[29],"learning,":[30],"algebraic":[31],"approaches":[32],"using":[33],"linear":[34],"algebra":[35],"or":[36],"Gr\u00f6bner":[37],"bases,":[38],"pseudo-Boolean":[40],"respectively).":[42],"There":[43],"is":[44,52,75],"also":[45],"a":[46],"discussion":[47],"extended":[49,62],"resolution":[50],"(which":[51],"closely":[53],"related":[54],"DRAT":[56],"logging)":[58],"Frege":[60,63],"more":[65],"generally.":[66],"An":[67],"ample":[68],"supply":[69],"references":[71],"for":[72,78],"further":[73],"reading":[74],"provided,":[76],"including":[77],"some":[79],"topics":[80],"omitted":[81],"in":[82],"this":[83],"chapter.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2021-02-15T00:00:00"}