{"id":"https://openalex.org/W4411523120","doi":"https://doi.org/10.1145/3728920","title":"Clause2Inv: A Generate-Combine-Check Framework for Loop Invariant Inference","display_name":"Clause2Inv: A Generate-Combine-Check Framework for Loop Invariant Inference","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4411523120","doi":"https://doi.org/10.1145/3728920"},"language":"en","primary_location":{"id":"doi:10.1145/3728920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3728920","pdf_url":null,"source":{"id":"https://openalex.org/S4404663975","display_name":"Proceedings of the ACM on software engineering.","issn_l":"2994-970X","issn":["2994-970X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Software Engineering","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/A5109458990","display_name":"Wan-Quan Cao","orcid":"https://orcid.org/0009-0006-2433-4920"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weining Cao","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0006-2433-4920","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113894236","display_name":"Guangyuan Wu","orcid":"https://orcid.org/0009-0003-4689-4097"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangyuan Wu","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0003-4689-4097","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Tangzhi Xu","orcid":"https://orcid.org/0009-0005-0438-5299"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tangzhi Xu","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0005-0438-5299","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068643894","display_name":"Yuan Yao","orcid":"https://orcid.org/0000-0002-6913-6542"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Yao","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-6913-6542","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071661810","display_name":"Hengfeng Wei","orcid":"https://orcid.org/0000-0002-0427-9710"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hengfeng Wei","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-0427-9710","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030747944","display_name":"Taolue Chen","orcid":"https://orcid.org/0000-0002-5993-1665"},"institutions":[{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Taolue Chen","raw_affiliation_strings":["Birkbeck University of London, London, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0002-5993-1665","affiliations":[{"raw_affiliation_string":"Birkbeck University of London, London, United Kingdom","institution_ids":["https://openalex.org/I98259816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041674680","display_name":"Xiaoxing Ma","orcid":"https://orcid.org/0000-0001-7970-1384"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoxing Ma","raw_affiliation_strings":["Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-7970-1384","affiliations":[{"raw_affiliation_string":"Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5109458990"],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":2.3578,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.89721698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"2","issue":"ISSTA","first_page":"1009","last_page":"1030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991000294685364,"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/T10142","display_name":"Formal Methods in Verification","score":0.9991000294685364,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.998199999332428,"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/inference","display_name":"Inference","score":0.7645226716995239},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.730719804763794},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6646642684936523},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.6252926588058472},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5763764381408691},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.45537906885147095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39849764108657837},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3717052936553955},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.28348106145858765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2568090558052063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1343185007572174}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.7645226716995239},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.730719804763794},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6646642684936523},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.6252926588058472},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5763764381408691},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45537906885147095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39849764108657837},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3717052936553955},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.28348106145858765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2568090558052063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1343185007572174},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3728920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3728920","pdf_url":null,"source":{"id":"https://openalex.org/S4404663975","display_name":"Proceedings of the ACM on software engineering.","issn_l":"2994-970X","issn":["2994-970X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on Software Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W145069693","https://openalex.org/W569478347","https://openalex.org/W1480909796","https://openalex.org/W1531054827","https://openalex.org/W1563374593","https://openalex.org/W1580330980","https://openalex.org/W1586497944","https://openalex.org/W1705210632","https://openalex.org/W1938285999","https://openalex.org/W1979711143","https://openalex.org/W2003463929","https://openalex.org/W2014764321","https://openalex.org/W2031373197","https://openalex.org/W2108776051","https://openalex.org/W2127574686","https://openalex.org/W2132661148","https://openalex.org/W2148177688","https://openalex.org/W2185676247","https://openalex.org/W2280703106","https://openalex.org/W2398327122","https://openalex.org/W2414616261","https://openalex.org/W2416392025","https://openalex.org/W2604799547","https://openalex.org/W2741361950","https://openalex.org/W2757602305","https://openalex.org/W2767715425","https://openalex.org/W2779005308","https://openalex.org/W2780276625","https://openalex.org/W2781303448","https://openalex.org/W2798609500","https://openalex.org/W2904362559","https://openalex.org/W3009272933","https://openalex.org/W3032926390","https://openalex.org/W3046688479","https://openalex.org/W3099870977","https://openalex.org/W3102168869","https://openalex.org/W3102469351","https://openalex.org/W4225922019","https://openalex.org/W4246691913","https://openalex.org/W4253311446","https://openalex.org/W4308644101","https://openalex.org/W4384155522","https://openalex.org/W4389520453","https://openalex.org/W4393942723","https://openalex.org/W4403536765","https://openalex.org/W6636134071"],"related_works":["https://openalex.org/W2026765907","https://openalex.org/W4307413753","https://openalex.org/W1975604118","https://openalex.org/W119766800","https://openalex.org/W2313450777","https://openalex.org/W2162268423","https://openalex.org/W2988498873","https://openalex.org/W4242826518","https://openalex.org/W2626139645","https://openalex.org/W2383711952"],"abstract_inverted_index":{"Loop":[0],"invariant":[1,71,88,112,129,184,195,204,260],"inference":[2,54,113,130,185,196,205,261],"is":[3,42,115,208,225],"a":[4,106,126,144,156],"fundamental,":[5],"yet":[6],"challenging,":[7],"problem":[8],"in":[9,25,31,48,92,105,263],"program":[10],"verification.":[11],"Recent":[12],"work":[13],"adopts":[14],"the":[15,26,32,53,69,74,82,85,93,101,110,133,149,161,167,216,222,236,241],"guess-and-check":[16,102,237],"framework,":[17,103,108,135],"where":[18,109],"candidate":[19,46,243],"loop":[20,87,111,128,183,259],"invariants":[21,47,244],"are":[22,233],"iteratively":[23],"generated":[24,172],"guess":[27],"step":[28],"and":[29,120,143,198,212,266],"verified":[30],"check":[33],"step.":[34],"A":[35],"major":[36],"challenge":[37],"of":[38,76,84,138,158,192,201,281,296],"this":[39],"general":[40],"framework":[41,224,238],"to":[43,73,99,154,170,227,287],"produce":[44],"high-quality":[45],"each":[49],"iteration":[50],"so":[51],"that":[52,62,179,250],"procedure":[55],"can":[56,284],"converge":[57],"quickly.":[58],"Empirically,":[59],"we":[60,124],"observe":[61],"existing":[63,182,217,230,258],"approaches":[64,231,262],"may":[65],"struggle":[66],"with":[67,254,276,291],"guessing":[68],"complete":[70],"due":[72],"complexity":[75],"logical":[77],"connectives,":[78],"but":[79],"usually,":[80],"all":[81],"clauses":[83,173],"correct":[86],"have":[89],"already":[90],"appeared":[91],"previous":[94,168],"guesses.":[95],"This":[96],"motivates":[97],"us":[98],"refine":[100],"resulting":[104],"generate-combine-check":[107,223],"task":[114],"divided":[116],"into":[117,174,245],"clause":[118,121,141,146,150,162],"generation":[119],"combination.":[122],"Specifically,":[123],"propose":[125],"novel":[127],"approach":[131,252],"under":[132,235],"new":[134],"which":[136,207,232,271],"consists":[137],"an":[139,277,292],"LLM-based":[140],"generator":[142],"counterexample-driven":[145],"combinator.":[147],"As":[148],"generator,":[151],"leverages":[152,164],"LLMs":[153],"generate":[155],"multitude":[157],"clauses;":[159],"as":[160],"combinator,":[163],"counterexamples":[165],"from":[166],"rounds":[169],"convert":[171],"invariants.":[175],"Our":[176],"experiments":[177],"show":[178],"significantly":[180],"outperforms":[181],"approaches.":[186],"For":[187,268],"example,":[188,269],"solved":[189,272],"312":[190],"(out":[191,200],"316)":[193],"linear":[194,274],"tasks":[197],"44":[199],"50)":[202],"nonlinear":[203],"tasks,":[206],"at":[209],"least":[210],"93":[211],"16":[213],"more":[214],"than":[215],"baselines,":[218],"respectively.":[219],"By":[220],"design,":[221],"flexible":[226],"accommodate":[228],"various":[229],"currently":[234],"by":[239],"splitting":[240],"guessed":[242],"clauses.":[246],"The":[247],"evaluation":[248],"shows":[249],"our":[251],"can,":[253],"minor":[255],"adaptation,":[256],"improve":[257],"both":[264],"effectiveness":[265],"efficiency.":[267],"Code2Inv":[270],"210":[273],"problems":[275,290],"average":[278,293],"solving":[279,294],"time":[280,295],"137.6":[282],"seconds":[283],"be":[285],"improved":[286],"solve":[288],"252":[289],"17.8":[297],"seconds.":[298]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}