{"id":"https://openalex.org/W3037338839","doi":"https://doi.org/10.1137/20m1351527","title":"Counting Solutions to Random CNF Formulas","display_name":"Counting Solutions to Random CNF Formulas","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3037338839","doi":"https://doi.org/10.1137/20m1351527","mag":"3037338839"},"language":"en","primary_location":{"id":"doi:10.1137/20m1351527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351527","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/files/222004589/randksat.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089713528","display_name":"Andreas Galanis","orcid":"https://orcid.org/0000-0003-3579-6531"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andreas Galanis","raw_affiliation_strings":["University of Oxford, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029293569","display_name":"Leslie Ann Goldberg","orcid":"https://orcid.org/0000-0003-1879-6089"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Leslie Ann Goldberg","raw_affiliation_strings":["University of Oxford, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100354396","display_name":"Heng Guo","orcid":"https://orcid.org/0000-0001-8199-5596"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Heng Guo","raw_affiliation_strings":["University of Edinburgh, Edinburgh, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Edinburgh, Edinburgh, United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022476435","display_name":"Kuan Yang","orcid":"https://orcid.org/0000-0002-9470-3887"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kuan Yang","raw_affiliation_strings":["University of Oxford, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089713528"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.7097,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7060502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"50","issue":"6","first_page":"1701","last_page":"1738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9930999875068665,"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/uniqueness","display_name":"Uniqueness","score":0.7280122637748718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6698323488235474},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5568860769271851},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.48839324712753296},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4443839192390442},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4381725788116455},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.33786267042160034},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33430689573287964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3249000310897827},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16326904296875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13788259029388428}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7280122637748718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6698323488235474},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5568860769271851},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.48839324712753296},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4443839192390442},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4381725788116455},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33786267042160034},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33430689573287964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3249000310897827},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16326904296875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13788259029388428},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1351527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1351527","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/b6e5ce43-2c43-4646-acf8-35ab42bdb305","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/b6e5ce43-2c43-4646-acf8-35ab42bdb305","pdf_url":"https://www.research.ed.ac.uk/files/222004589/randksat.pdf","source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Galanis, A, Goldberg, L A, Guo, H & Yang, K 2021, 'Counting Solutions to Random CNF Formulas', SIAM Journal on Computing, vol. 50, no. 6, pp. 1701-1738. https://doi.org/10.1137/20M1351527","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/b6e5ce43-2c43-4646-acf8-35ab42bdb305","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/b6e5ce43-2c43-4646-acf8-35ab42bdb305","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Galanis, A, Goldberg, L A, Guo, H & Yang, K 2021, 'Counting Solutions to Random CNF Formulas', SIAM Journal on Computing, vol. 50, no. 6, pp. 1701-1738. https://doi.org/10.1137/20M1351527","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:publications/b6e5ce43-2c43-4646-acf8-35ab42bdb305","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/b6e5ce43-2c43-4646-acf8-35ab42bdb305","pdf_url":"https://www.research.ed.ac.uk/files/222004589/randksat.pdf","source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Galanis, A, Goldberg, L A, Guo, H & Yang, K 2021, 'Counting Solutions to Random CNF Formulas', SIAM Journal on Computing, vol. 50, no. 6, pp. 1701-1738. https://doi.org/10.1137/20M1351527","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2824819309","display_name":null,"funder_award_id":"334828","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G8082076833","display_name":null,"funder_award_id":"947778","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3037338839.pdf","grobid_xml":"https://content.openalex.org/works/W3037338839.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1518885151","https://openalex.org/W1559492868","https://openalex.org/W1976579329","https://openalex.org/W1977759320","https://openalex.org/W2000931246","https://openalex.org/W2051336598","https://openalex.org/W2063428816","https://openalex.org/W2072870176","https://openalex.org/W2090216341","https://openalex.org/W2105860081","https://openalex.org/W2107779545","https://openalex.org/W2109693504","https://openalex.org/W2128452148","https://openalex.org/W2156584294","https://openalex.org/W2296503402","https://openalex.org/W2479814928","https://openalex.org/W2522859079","https://openalex.org/W2566005205","https://openalex.org/W2570121038","https://openalex.org/W2914272038","https://openalex.org/W2938658492","https://openalex.org/W2952323594","https://openalex.org/W2962726369","https://openalex.org/W2966749622","https://openalex.org/W3013409926","https://openalex.org/W3124429033"],"related_works":["https://openalex.org/W41352805","https://openalex.org/W17758310","https://openalex.org/W2320053","https://openalex.org/W34290013","https://openalex.org/W40006772","https://openalex.org/W31696729","https://openalex.org/W9380987","https://openalex.org/W45374770","https://openalex.org/W17277841","https://openalex.org/W314045"],"abstract_inverted_index":{"We":[0],"give":[1],"the":[2,9,14,18,21,32,36,48,58,63,93,111],"first":[3],"e\ufb00icient":[4],"algorithm":[5,30,67],"to":[6,40,55,74,90,103],"approximately":[7],"count":[8],"number":[10],"of":[11,20,35,95],"solutions":[12],"in":[13,86],"randomk-SAT":[15],"model":[16,37],"when":[17],"density":[19],"formula":[22],"scales":[23],"exponentially":[24],"with":[25,79],"k.The":[26],"best":[27],"previous":[28],"counting":[29],"for":[31,62,76,92],"permissive":[33],"version":[34],"was":[38,45],"due":[39],"Montanari":[41],"and":[42,44,105],"Shah":[43],"based":[46],"on":[47],"correlation":[49],"decay":[50],"method,":[51],"which":[52,106],"works":[53],"up":[54],"densities":[56],"(1+<i>o</i><sub>k</sub>(1))2log<i>k</i>/<i>k</i>,":[57],"Gibbs":[59],"uniqueness":[60],"threshold":[61],"model.":[64],"Instead,":[65],"our":[66,87],"harnesses":[68],"a":[69],"recent":[70],"technique":[71],"by":[72],"Moitra":[73],"work":[75],"random":[77],"formulas":[78],"much":[80],"higher":[81],"densities.":[82],"The":[83],"main":[84],"challenge":[85],"setting":[88],"is":[89],"account":[91],"presence":[94],"high-degree":[96],"variables":[97],"whose":[98],"marginal":[99],"distributions":[100],"are":[101],"hard":[102],"control":[104],"cause":[107],"significant":[108],"correlations":[109],"within":[110],"formula.":[112]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2020-07-02T00:00:00"}
