{"id":"https://openalex.org/W7162444534","doi":"https://doi.org/10.48550/arxiv.2605.24845","title":"Solving Combinatorial Counting Problems with Weighted First-Order Model Counting","display_name":"Solving Combinatorial Counting Problems with Weighted First-Order Model Counting","publication_year":2026,"publication_date":"2026-05-24","ids":{"openalex":"https://openalex.org/W7162444534","doi":"https://doi.org/10.48550/arxiv.2605.24845"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.24845","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24845","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.24845","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137025785","display_name":"Yuanhong Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yuanhong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101069493","display_name":"Juhua Pu","orcid":"https://orcid.org/0000-0003-3866-8703"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pu, Juhua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137011445","display_name":"Yuxu Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Yuxu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129738945","display_name":"Yuyi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yuyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021262042","display_name":"Ond\u0159ej Ku\u017eelka","orcid":"https://orcid.org/0000-0002-6523-9114"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ku\u017eelka, Ond\u0159ej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.2526000142097473,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.2526000142097473,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.04430000111460686,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10799","display_name":"Data Visualization and Analytics","score":0.039500001817941666,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/counting-problem","display_name":"Counting problem","score":0.7804999947547913},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.5702999830245972},{"id":"https://openalex.org/keywords/constraint-satisfaction-problem","display_name":"Constraint satisfaction problem","score":0.5054000020027161},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4681999981403351},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4602999985218048},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.4438999891281128},{"id":"https://openalex.org/keywords/true-quantified-boolean-formula","display_name":"True quantified Boolean formula","score":0.4034000039100647},{"id":"https://openalex.org/keywords/denotational-semantics","display_name":"Denotational semantics","score":0.39730000495910645}],"concepts":[{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.7804999947547913},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.5702999830245972},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.5054000020027161},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4778999984264374},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44519999623298645},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C207648694","wikidata":"https://www.wikidata.org/wiki/Q1189746","display_name":"Denotational semantics","level":4,"score":0.39730000495910645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3953999876976013},{"id":"https://openalex.org/C115908005","wikidata":"https://www.wikidata.org/wiki/Q2668364","display_name":"Combinatorial explosion","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34549999237060547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.3206999897956848},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C2781104640","wikidata":"https://www.wikidata.org/wiki/Q11827313","display_name":"Counting process","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C2987825933","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorial analysis","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C203208320","wikidata":"https://www.wikidata.org/wiki/Q5150830","display_name":"Combinatorial search","level":4,"score":0.2800000011920929},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2563999891281128},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.24845","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24845","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.24845","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.24845","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.4397316575050354}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Combinatorial":[0],"counting":[1,45,54,64,83,114,134,175],"problems":[2,181],"pervade":[3],"artificial":[4],"intelligence,":[5],"statistics,":[6],"and":[7,23,92,98,116,123,161,164,196],"discrete":[8],"mathematics.":[9],"Whether":[10],"the":[11,50,57,76,149,155,186],"task":[12],"is":[13,202],"enumerating":[14],"subsets,":[15],"multisets,":[16],"permutations,":[17],"partitions,":[18,91],"or":[19,46],"compositions":[20],"under":[21],"structural":[22],"arithmetic":[24,99],"constraints,":[25],"solving":[26,199],"it":[27],"remains":[28],"a":[29,69,111,117,130,170,197],"stubbornly":[30],"manual":[31],"exercise.":[32],"Closed-form":[33],"derivations":[34],"are":[35,75],"powerful":[36],"but":[37],"brittle,":[38],"while":[39],"naive":[40],"encodings":[41],"to":[42,110,129,182],"propositional":[43],"model":[44,133],"constraint":[47],"satisfaction":[48],"destroy":[49],"exchangeability":[51],"that":[52,79,185,201],"makes":[53],"tractable":[55],"in":[56,81],"first":[58],"place.":[59],"We":[60],"present":[61],"Cofola":[62,108,192],"(COmbinatorial":[63],"LAnguage":[65],"with":[66,95,138],"First-Order":[67],"logic),":[68],"typed":[70],"declarative":[71],"language":[72],"whose":[73],"primitives":[74],"combinatorial":[77,113,174],"objects":[78],"recur":[80],"everyday":[82],"questions,":[84],"including":[85],"sets,":[86],"bags,":[87],"tuples,":[88],"sequences,":[89],"circles,":[90],"compositions,":[93],"together":[94],"natural":[96],"relational":[97],"constraints":[100],"over":[101],"them.":[102],"A":[103],"denotational":[104],"semantics":[105],"maps":[106],"every":[107],"program":[109],"well-defined":[112],"problem,":[115],"three-phase":[118],"compilation":[119],"pipeline":[120,200],"(preprocessing,":[121],"decomposition,":[122],"symmetry-preserving":[124],"encoding)":[125],"reduces":[126],"this":[127],"problem":[128],"weighted":[131],"first-order":[132],"(WFOMC)":[135],"instance":[136],"augmented":[137],"coefficient-extraction":[139],"constraints.":[140],"To":[141],"stay":[142],"inside":[143],"known":[144],"domain-liftable":[145],"fragments":[146],"whenever":[147],"possible,":[148],"encoding":[150],"groups":[151],"indistinguishable":[152],"entities,":[153],"breaks":[154],"symmetry":[156],"of":[157,172],"unordered":[158],"groupings":[159],"lexicographically,":[160],"encodes":[162],"sequences":[163],"circles":[165],"via":[166],"order":[167],"axioms.":[168],"On":[169],"suite":[171],"representative":[173],"problems,":[176],"ranging":[177],"from":[178],"textbook":[179],"math":[180],"multi-object":[183],"scenarios":[184],"closest":[187],"prior":[188],"framework":[189],"cannot":[190],"express,":[191],"produces":[193],"concise":[194],"specifications":[195],"uniform":[198],"practical":[203],"end-to-end.":[204]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-27T00:00:00"}