{"id":"https://openalex.org/W4387878066","doi":"https://doi.org/10.3233/faia230707","title":"On the Density of States of Boolean Formulas1","display_name":"On the Density of States of Boolean Formulas1","publication_year":2023,"publication_date":"2023-10-19","ids":{"openalex":"https://openalex.org/W4387878066","doi":"https://doi.org/10.3233/faia230707"},"language":"en","primary_location":{"id":"doi:10.3233/faia230707","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia230707","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA230707","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","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":true,"oa_status":"hybrid","oa_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA230707","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039752849","display_name":"Carlos Ans\u00f3tegui","orcid":"https://orcid.org/0000-0001-7727-2766"},"institutions":[{"id":"https://openalex.org/I15766328","display_name":"Universitat de Lleida","ror":"https://ror.org/050c3cw24","country_code":"ES","type":"education","lineage":["https://openalex.org/I15766328"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carlos Ans\u00f3tegui","raw_affiliation_strings":["Universitat de Lleida (DIEI, UdL), Lleida, Spain"],"raw_orcid":"https://orcid.org/0000-0001-7727-2766","affiliations":[{"raw_affiliation_string":"Universitat de Lleida (DIEI, UdL), Lleida, Spain","institution_ids":["https://openalex.org/I15766328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022258975","display_name":"Mar\u0131\u0301a Luisa Bonet","orcid":"https://orcid.org/0000-0003-1646-7177"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda Luisa Bonet","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Catalunya (CS, UPC), Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0003-1646-7177","affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya (CS, UPC), Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027212883","display_name":"Jordi Levy","orcid":"https://orcid.org/0009-0002-4337-2608"},"institutions":[{"id":"https://openalex.org/I4210131846","display_name":"Artificial Intelligence Research Institute","ror":"https://ror.org/03c0ach84","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210131846"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jordi Levy","raw_affiliation_strings":["Artificial Intelligence Research Institute (IIIA, CSIC), Bellaterra, Spain"],"raw_orcid":"https://orcid.org/0000-0001-5883-5746","affiliations":[{"raw_affiliation_string":"Artificial Intelligence Research Institute (IIIA, CSIC), Bellaterra, Spain","institution_ids":["https://openalex.org/I4210131846"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039752849"],"corresponding_institution_ids":["https://openalex.org/I15766328"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.52654046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"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/T10142","display_name":"Formal Methods in Verification","score":0.9872999787330627,"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":0.9872999787330627,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9757000207901001,"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":0.9689000248908997,"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/solver","display_name":"Solver","score":0.6801105737686157},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.6713430881500244},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.611892819404602},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5857200622558594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5417000651359558},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47939276695251465},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4277814030647278},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4134466350078583},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39933598041534424},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.3409789800643921},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2242986261844635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07653549313545227}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6801105737686157},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6713430881500244},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.611892819404602},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5857200622558594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5417000651359558},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47939276695251465},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4277814030647278},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4134466350078583},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39933598041534424},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.3409789800643921},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2242986261844635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07653549313545227},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":2,"locations":[{"id":"doi:10.3233/faia230707","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia230707","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA230707","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},{"id":"pmh:oai:repositori.udl.cat:10459.1/467372","is_oa":true,"landing_page_url":"https://hdl.handle.net/10459.1/467372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400812","display_name":"Repositori ObertUDL (University of Lleida)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766328","host_organization_name":"Universitat de Lleida","host_organization_lineage":["https://openalex.org/I15766328"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.3233/faia230707","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia230707","pdf_url":"https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA230707","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6600000262260437}],"awards":[{"id":"https://openalex.org/G2764623439","display_name":null,"funder_award_id":"PID2022-138506NB-C21","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6891804154","display_name":null,"funder_award_id":"PID2019-109137GB-C21","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387878066.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W16743356","https://openalex.org/W179198942","https://openalex.org/W189719929","https://openalex.org/W1481524367","https://openalex.org/W1511963917","https://openalex.org/W1513363711","https://openalex.org/W1535430927","https://openalex.org/W1537730723","https://openalex.org/W1546201437","https://openalex.org/W1565010992","https://openalex.org/W1571334244","https://openalex.org/W1576973534","https://openalex.org/W1578612406","https://openalex.org/W1607840088","https://openalex.org/W1686746446","https://openalex.org/W1829927364","https://openalex.org/W1863234917","https://openalex.org/W2012413542","https://openalex.org/W2033274122","https://openalex.org/W2066514569","https://openalex.org/W2071319337","https://openalex.org/W2080267935","https://openalex.org/W2100609826","https://openalex.org/W2114267503","https://openalex.org/W2116758077","https://openalex.org/W2118943303","https://openalex.org/W2149018851","https://openalex.org/W2279529505","https://openalex.org/W4300624830","https://openalex.org/W6634177029","https://openalex.org/W6637293339"],"related_works":["https://openalex.org/W2301405299","https://openalex.org/W139322340","https://openalex.org/W4285605366","https://openalex.org/W2118943303","https://openalex.org/W3150741540","https://openalex.org/W4253759203","https://openalex.org/W2085380335","https://openalex.org/W4386614288","https://openalex.org/W2115480761","https://openalex.org/W2883069340"],"abstract_inverted_index":{"Given":[0],"a":[1,17,116,120,124,148,154],"CNF":[2],"formula":[3,117,125],"with":[4,191],"m":[5],"clauses,":[6],"and":[7,119],"an":[8,178],"integer":[9],"k,":[10],"where":[11,78],"0":[12],"\u2264":[13,15],"k":[14,32],"m,":[16],"density":[18,45,71,98,173],"of":[19,26,34,46,48,72,74,87,99,131,133,138,145,161,174],"states":[20,47,73,175],"procedure":[21],"will":[22],"count":[23,158],"the":[24,35,39,44,54,70,79,96,105,129,136,159,172,183],"number":[25,130,137],"truth":[27],"assignments":[28,139],"that":[29,91,140],"falsify":[30,141],"exactly":[31,142],"clauses":[33,144],"formula.":[36],"We":[37],"present":[38,102],"first":[40,55,106],"approach":[41,164],"to":[42,94,108,157,169,189],"compute":[43,95,170],"Boolean":[49,75,193],"formulas":[50],"exactly.":[51],"This":[52,163],"is":[53,92,104,135,151],"non-trivial":[56],"result":[57],"on":[58],"this":[59,110],"known":[60],"hard":[61],"problem.":[62],"There":[63],"are":[64,84],"previous":[65],"approaches":[66],"for":[67],"computing":[68],"approximately":[69,171],"Formulas":[76],"[1,2],":[77],"authors":[80],"point":[81],"out":[82],"they":[83],"not":[85],"aware":[86],"any":[88],"complete":[89],"solver":[90,150],"able":[93],"exact":[97],"states.":[100],"The":[101,112],"work":[103],"step":[107],"fill":[109],"gap.":[111],"idea":[113],"is,":[114],"given":[115],"\u03c6":[118],"parameter":[121],"c,":[122],"construct":[123],"\u03c6c":[126,134],"such":[127],"that,":[128],"models":[132,160],"c":[143],"\u03c6.":[146],"Then,":[147],"#SAT":[149,180],"used":[152,168],"as":[153],"black":[155],"box":[156],"\u03c6c.":[162],"can":[165,185],"be":[166,186],"also":[167],"by":[176],"using":[177],"approximate":[179],"solver.":[181],"Finally,":[182],"method":[184],"extended":[187],"trivially":[188],"deal":[190],"Weighted":[192],"formulas.":[194]},"counts_by_year":[],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2023-10-24T00:00:00"}