{"id":"https://openalex.org/W2130229234","doi":"https://doi.org/10.1109/lics.2002.1029840","title":"Unsatisfiable random formulas are hard to certify","display_name":"Unsatisfiable random formulas are hard to certify","publication_year":2003,"publication_date":"2003-06-25","ids":{"openalex":"https://openalex.org/W2130229234","doi":"https://doi.org/10.1109/lics.2002.1029840","mag":"2130229234"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2002.1029840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2002.1029840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th Annual IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-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/A5003671114","display_name":"Albert Atserias","orcid":"https://orcid.org/0000-0002-3732-1989"},"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":true,"raw_author_name":"A. Atserias","raw_affiliation_strings":["Universitat Polilt\u00e8cnica de Catalunya, Barcelona, Spain","Univ. Politecnica de Catalunya, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Polilt\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Univ. Politecnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003671114"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":1.4039,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85608527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":null,"first_page":"325","last_page":"334"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9973999857902527,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9958999752998352,"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9670581817626953},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6830688118934631},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.6482962965965271},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6405899524688721},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.629387378692627},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5449749827384949},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.5321124196052551},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5216736793518066},{"id":"https://openalex.org/keywords/conservative-extension","display_name":"Conservative extension","score":0.4758155941963196},{"id":"https://openalex.org/keywords/datalog","display_name":"Datalog","score":0.4599882662296295},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.44848477840423584},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4189738631248474},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32384979724884033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2853301465511322},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.28347912430763245},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.18615198135375977},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.08493432402610779}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9670581817626953},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6830688118934631},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.6482962965965271},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6405899524688721},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.629387378692627},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5449749827384949},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.5321124196052551},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5216736793518066},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.4758155941963196},{"id":"https://openalex.org/C148230440","wikidata":"https://www.wikidata.org/wiki/Q1172264","display_name":"Datalog","level":2,"score":0.4599882662296295},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.44848477840423584},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4189738631248474},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32384979724884033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2853301465511322},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.28347912430763245},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.18615198135375977},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.08493432402610779},{"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/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lics.2002.1029840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2002.1029840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 17th Annual IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.11.5491","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.5491","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.ucsc.edu/~atserias/pagina/papers/lics02/r3sat1.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W25304578","https://openalex.org/W1963913579","https://openalex.org/W1969966778","https://openalex.org/W1970557422","https://openalex.org/W1988083342","https://openalex.org/W2026745535","https://openalex.org/W2041857712","https://openalex.org/W2044722214","https://openalex.org/W2069767473","https://openalex.org/W2073227282","https://openalex.org/W2075335084","https://openalex.org/W2084384424","https://openalex.org/W2085536555","https://openalex.org/W2090008352","https://openalex.org/W2091969666","https://openalex.org/W2126420408","https://openalex.org/W2131459042","https://openalex.org/W2132240307","https://openalex.org/W2136558174","https://openalex.org/W2136687801","https://openalex.org/W2138778293","https://openalex.org/W2170743240","https://openalex.org/W2172068139","https://openalex.org/W4212857488","https://openalex.org/W4235934183","https://openalex.org/W4254380579","https://openalex.org/W6601043544"],"related_works":["https://openalex.org/W2063658344","https://openalex.org/W2062912795","https://openalex.org/W2610304232","https://openalex.org/W4301514548","https://openalex.org/W2963321374","https://openalex.org/W129584612","https://openalex.org/W2786710967","https://openalex.org/W3207331746","https://openalex.org/W1516535258","https://openalex.org/W2130229234"],"abstract_inverted_index":{"We":[0],"prove":[1,143],"that":[2,8,57,80,99,121,144,151],"every":[3],"property":[4],"of":[5,30,42,76,95,104,160,180,188],"3CNF":[6,60,90,154,190],"formulas":[7,21,191],"implies":[9],"unsatisfiability":[10],"and":[11,35,62,83,108,135,169,192],"is":[12,39,98],"expressible":[13],"in":[14,49,174],"Datalog":[15],"has":[16,156],"asymptotic":[17],"probability":[18],"zero":[19],"when":[20],"are":[22],"randomly":[23],"generated":[24],"by":[25],"taking":[26],"6n":[27],"non-trivial":[28],"clauses":[29],"exactly":[31],"three":[32],"literals":[33],"uniformly":[34],"independently.":[36],"Our":[37],"result":[38,97,168],"a":[40,44,63,68,88,147,157,164],"consequence":[41,165],"designing":[43],"winning":[45,72],"strategy":[46,73],"for":[47,185],"Duplicator":[48,122],"the":[50,55,59,102,124,129,132,136,170,181,193],"existential":[51,125],"k-pebble":[52],"game":[53,127],"on":[54,87,128],"structure":[56,66,130,138],"encodes":[58],"formula":[61,155],"fixed":[64],"template":[65,137],"encoding":[67,131],"satisfiable":[69],"formula.":[70,91],"The":[71],"makes":[74],"use":[75],"certain":[77],"extension":[78],"axioms":[79],"we":[81,119,141,176],"introduce":[82],"hold":[84],"almost":[85],"surely":[86],"random":[89,189],"An":[92],"interesting":[93],"feature":[94],"our":[96,167],"it":[100],"brings":[101],"fields":[103],"propositional":[105],"proof":[106],"complexity":[107],"finite":[109],"model":[110],"theory":[111],"together.":[112],"To":[113],"make":[114],"this":[115],"connection":[116],"more":[117],"explicit,":[118],"show":[120],"wins":[123],"pebble":[126],"pigeonhole":[133,194],"principle":[134],"above.":[139],"Moreover,":[140],"also":[142],"there":[145],"exists":[146],"2k-Datalog":[148],"program":[149],"expressing":[150],"an":[152],"input":[153],"resolution":[158,186],"refutation":[159],"width":[161],"k.":[162],"As":[163],"to":[166],"known":[171],"size-width":[172],"relationship":[173],"resolution,":[175],"obtain":[177],"new":[178],"proofs":[179],"exponential":[182],"lower":[183],"bounds":[184],"refutations":[187],"principle.":[195]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
