{"id":"https://openalex.org/W7162688986","doi":"https://doi.org/10.48550/arxiv.2605.28602","title":"Satisfiability Solving with LLMs: A Matched-Pair Evaluation of Reasoning Capability","display_name":"Satisfiability Solving with LLMs: A Matched-Pair Evaluation of Reasoning Capability","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162688986","doi":"https://doi.org/10.48550/arxiv.2605.28602"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.28602","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.28602","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137237940","display_name":"Leizhen Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Leizhen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137208287","display_name":"Shuhan Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Shuhan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137197613","display_name":"Sheng Chen","orcid":"https://orcid.org/0009-0001-7186-4960"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Sheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.26579999923706055,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.26579999923706055,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10181","display_name":"Natural Language Processing Techniques","score":0.14579999446868896,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.10450000315904617,"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/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.6729999780654907},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6662999987602234},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5200999975204468},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.45840001106262207},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.4390999972820282},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.42660000920295715},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3856000006198883},{"id":"https://openalex.org/keywords/dpll-algorithm","display_name":"DPLL algorithm","score":0.3668999969959259}],"concepts":[{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6729999780654907},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5712000131607056},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5184000134468079},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.4390999972820282},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.42660000920295715},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37439998984336853},{"id":"https://openalex.org/C143936061","wikidata":"https://www.wikidata.org/wiki/Q2030088","display_name":"DPLL algorithm","level":4,"score":0.3668999969959259},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.3497999906539917},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3179999887943268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3133000135421753},{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.27730000019073486},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.28602","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.28602","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.7346649169921875,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large":[0],"language":[1],"models":[2,53,79,144,186],"(LLMs)":[3],"are":[4],"increasingly":[5],"used":[6],"for":[7,184,210],"tasks":[8],"that":[9,72,204,214],"implicitly":[10],"reduce":[11],"to":[12,46,88,137,162,167],"Boolean":[13],"satisfiability":[14],"(SAT),":[15],"yet":[16],"their":[17],"reasoning":[18],"ability":[19],"on":[20,31,117,173,176,187],"SAT":[21,67,205],"remains":[22],"unclear.":[23],"We":[24,50,70],"present":[25],"a":[26,113,207,220],"systematic":[27],"study":[28],"of":[29,104,134,192],"LLMs":[30],"2-SAT":[32],"and":[33,42,61,98,121,148,165,175,213,223],"3-SAT,":[34],"together":[35,124],"with":[36,125,150,217],"two":[37],"canonical":[38],"reductions,":[39],"Vertex":[40,163],"Cover":[41,164],"discrete":[43,168],"3D":[44,169],"packing,":[45],"probe":[47,209],"representation-invariant":[48],"reasoning.":[49],"first":[51],"evaluate":[52],"using":[54],"conventional":[55,227],"metrics,":[56],"including":[57],"accuracy,":[58],"precision,":[59],"recall,":[60],"F1,":[62],"as":[63,65,101],"well":[64],"the":[66,90,95,102,177],"phase-transition":[68],"setting.":[69],"find":[71],"these":[73],"metrics":[74],"can":[75],"be":[76,138],"misleading:":[77],"many":[78],"obtain":[80],"high":[81],"scores":[82],"by":[83,159],"over-predicting":[84],"satisfiable":[85,120],"formulas,":[86],"fail":[87],"reproduce":[89],"classical":[91],"easy-hard-easy":[92],"signature":[93],"around":[94],"3-SAT":[96,166],"threshold,":[97],"degrade":[99],"sharply":[100],"number":[103],"variables":[105],"grows.":[106],"To":[107],"address":[108],"this":[109],"problem,":[110],"we":[111,155],"introduce":[112],"paired-formula":[114],"protocol":[115],"based":[116],"minimally":[118],"different":[119],"unsatisfiable":[122],"instances,":[123,193],"Accurate":[126],"Differentiation":[127],"Rate":[128],"(ADR),":[129],"which":[130],"requires":[131],"both":[132],"members":[133],"each":[135],"pair":[136],"classified":[139],"correctly.":[140],"ADR":[141,218],"separates":[142],"reasoning-oriented":[143],"from":[145],"heuristic":[146],"ones":[147],"correlates":[149],"witness":[151],"validity.":[152],"Beyond":[153],"CNF,":[154],"test":[156],"cross-representation":[157],"consistency":[158],"converting":[160],"CNF":[161,174],"packing.":[170],"Model":[171],"decisions":[172],"corresponding":[178],"graph":[179],"or":[180],"packing":[181],"instances":[182],"agree":[183],"most":[185],"more":[188,221],"than":[189,226],"80":[190],"percent":[191],"suggesting":[194],"stable":[195],"decision":[196],"rules":[197],"across":[198],"representations.":[199],"Overall,":[200],"our":[201],"results":[202],"show":[203],"is":[206],"conservative":[208],"LLM":[211],"reasoning,":[212],"paired":[215],"evaluation":[216],"provides":[219],"faithful":[222],"representation-robust":[224],"assessment":[225],"metrics.":[228]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-29T00:00:00"}
