{"id":"https://openalex.org/W2083392982","doi":"https://doi.org/10.1017/s0963548309990356","title":"On the Random Satisfiable Process","display_name":"On the Random Satisfiable Process","publication_year":2009,"publication_date":"2009-08-20","ids":{"openalex":"https://openalex.org/W2083392982","doi":"https://doi.org/10.1017/s0963548309990356","mag":"2083392982"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548309990356","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548309990356","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"MICHAEL KRIVELEVICH","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel (e-mail:","School of mathematical sciences, tel aviv university, tel aviv, israel (e-mail: krivelev@post.tau.ac.il)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel (e-mail:","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of mathematical sciences, tel aviv university, tel aviv, israel (e-mail: krivelev@post.tau.ac.il)","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066741544","display_name":"Benny Sudakov","orcid":"https://orcid.org/0000-0003-3307-9475"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I2799798094","display_name":"UCLA Health","ror":"https://ror.org/01d88se56","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799798094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BENNY SUDAKOV","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, USA (e-mail:","Department of mathematics, ucla, los angeles, usa (e-mail: bsudakov@math.ucla.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, USA (e-mail:","institution_ids":["https://openalex.org/I161318765","https://openalex.org/I2799798094"]},{"raw_affiliation_string":"Department of mathematics, ucla, los angeles, usa (e-mail: bsudakov@math.ucla.edu)#TAB#","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067064621","display_name":"Dan Vilenchik","orcid":"https://orcid.org/0000-0002-3895-688X"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I2799798094","display_name":"UCLA Health","ror":"https://ror.org/01d88se56","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799798094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DAN VILENCHIK","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, USA (e-mail:","Department of mathematics, ucla, los angeles, usa (e-mail: danny.vilenchik@gmail.com)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, USA (e-mail:","institution_ids":["https://openalex.org/I161318765","https://openalex.org/I2799798094"]},{"raw_affiliation_string":"Department of mathematics, ucla, los angeles, usa (e-mail: danny.vilenchik@gmail.com)#TAB#","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3205,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.62210797,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"5","first_page":"775","last_page":"801"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.998199999332428,"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/T11106","display_name":"Data Management and Algorithms","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/combinatorics","display_name":"Combinatorics","score":0.7755368947982788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.712515115737915},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6454944610595703},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5581769347190857},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5547048449516296},{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.5148057341575623},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5071218013763428},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.4967578053474426},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4341747462749481},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.42864373326301575},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40817147493362427}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7755368947982788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.712515115737915},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6454944610595703},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5581769347190857},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5547048449516296},{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.5148057341575623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5071218013763428},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.4967578053474426},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4341747462749481},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.42864373326301575},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40817147493362427},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548309990356","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548309990356","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.139.8355","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.8355","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bsudakov/random-sat-model.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.3966","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.3966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~krivelev/newSAT.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.8895","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.8895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bsudakov/random-sat-model.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.4901","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.4901","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0807.4326.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W63271104","https://openalex.org/W1504923017","https://openalex.org/W1559492868","https://openalex.org/W1569752386","https://openalex.org/W1599622173","https://openalex.org/W1980276492","https://openalex.org/W1983171306","https://openalex.org/W1994098212","https://openalex.org/W1999032440","https://openalex.org/W2013024636","https://openalex.org/W2033652300","https://openalex.org/W2036265926","https://openalex.org/W2063428816","https://openalex.org/W2068871408","https://openalex.org/W2079035346","https://openalex.org/W2115831572","https://openalex.org/W2118626701","https://openalex.org/W2128765501","https://openalex.org/W2134147092","https://openalex.org/W2134771417","https://openalex.org/W2136227650","https://openalex.org/W2139919528","https://openalex.org/W2159080219","https://openalex.org/W2161257095","https://openalex.org/W2496163386","https://openalex.org/W2740374147","https://openalex.org/W2949527520","https://openalex.org/W3105442588","https://openalex.org/W4231289884","https://openalex.org/W4250225190","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W2405987656","https://openalex.org/W2054383364","https://openalex.org/W2979276937","https://openalex.org/W2049398763","https://openalex.org/W2279485703","https://openalex.org/W2016416733","https://openalex.org/W4243953177","https://openalex.org/W1989366892","https://openalex.org/W3100313843","https://openalex.org/W4235475206"],"abstract_inverted_index":{"In":[0],"this":[1,70,163,206],"work":[2],"we":[3,190,209],"suggest":[4],"a":[5,95,122,159,186,202,246,252],"new":[6,51],"model":[7,157],"for":[8,119,135,255],"generating":[9],"random":[10,87],"satisfiable":[11],"k":[12,184],"-CNF":[13],"formulas.":[14,18,257],"To":[15],"generate":[16],"such":[17,149,256],"randomly":[19],"permute":[20],"all":[21,213,223,240],"$2^k\\binom{n}{k}$":[22],"possible":[23],"clauses":[24,45,84],"over":[25,43,75],"the":[26,39,44,61,67,73,81,86,104,166,195,198,233,236],"variables":[27,234],"x":[28,33],"1":[29],",.":[30],".":[31],".,":[32],"n":[34,229,231],",":[35,179],"and":[36,115,126,131,137,152,222],"starting":[37],"from":[38],"empty":[40],"formula,":[41],"go":[42,55],"one":[46,220],"by":[47,113,128],"one,":[48],"including":[49],"each":[50],"clause":[52],"as":[53,150,173],"you":[54],"along":[56],"if,":[57],"after":[58,78],"its":[59],"addition,":[60],"formula":[62,204],"remains":[63],"satisfiable.":[64],"We":[65,243],"study":[66,110],"evolution":[68],"of":[69,106,162,197,201,232],"process,":[71],"namely":[72],"distribution":[74],"formulas":[76],"obtained":[77],"scanning":[79],"through":[80],"first":[82],"m":[83,176,227],"(in":[85],"permutation's":[88],"order).":[89],"Random":[90],"processes":[91],"with":[92,121],"conditioning":[93],"on":[94],"certain":[96],"property":[97],"being":[98],"respected":[99],"are":[100,191,216],"widely":[101],"studied":[102],"in":[103,117,133,205,219,239],"context":[105],"graph":[107,144],"properties.":[108],"This":[109],"was":[111],"pioneered":[112],"Ruci\u0144ski":[114],"Wormald":[116],"1992":[118],"graphs":[120],"fixed":[123],"degree":[124],"sequence,":[125],"also":[127,244],"Erd\u0151s,":[129],"Suen":[130],"Winkler":[132],"1995":[134],"triangle-free":[136],"bipartite":[138],"graphs.":[139],"Since":[140],"then":[141],"many":[142],"other":[143],"properties":[145],"have":[146],"been":[147],"studied,":[148],"planarity":[151],"H":[153],"-freeness.":[154],"Thus":[155],"our":[156],"is":[158,172],"natural":[160],"extension":[161],"approach":[164],"to":[165,193],"satisfiability":[167],"setting.":[168],"Our":[169],"main":[170],"contribution":[171],"follows.":[174],"For":[175],"\u2265":[177],"cn":[178],"c":[180,182],"=":[181],"(":[183],")":[185,230],"sufficiently":[187],"large":[188],"constant,":[189],"able":[192],"characterize":[194],"structure":[196],"solution":[199],"space":[200],"typical":[203],"distribution.":[207],"Specifically,":[208],"show":[210],"that":[211,249],"typically":[212],"satisfying":[214,241,253],"assignments":[215],"essentially":[217],"clustered":[218],"cluster,":[221],"but":[224],"e":[225],"\u2212\u03a9(":[226],"/":[228],"take":[235],"same":[237],"value":[238],"assignments.":[242],"describe":[245],"polynomial-time":[247],"algorithm":[248],"finds":[250],"w.h.p.":[251],"assignment":[254]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}