{"id":"https://openalex.org/W4405549773","doi":"https://doi.org/10.1145/3708559","title":"Synthesizing Invariants for Polynomial Programs by Semidefinite Programming","display_name":"Synthesizing Invariants for Polynomial Programs by Semidefinite Programming","publication_year":2024,"publication_date":"2024-12-18","ids":{"openalex":"https://openalex.org/W4405549773","doi":"https://doi.org/10.1145/3708559"},"language":"en","primary_location":{"id":"doi:10.1145/3708559","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3708559","pdf_url":null,"source":{"id":"https://openalex.org/S41449414","display_name":"ACM Transactions on Programming Languages and Systems","issn_l":"0164-0925","issn":["0164-0925","1558-4593"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"ACM Transactions on Programming Languages and Systems","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/A5100584460","display_name":"Hao Wu","orcid":"https://orcid.org/0000-0001-9368-4744"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hao Wu","raw_affiliation_strings":["State Key Lab. of Computer Sciences, Institute of Software, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","Institute of Software, Chinese Academy of Sciences & University of CAS, China"],"raw_orcid":"https://orcid.org/0000-0001-9368-4744","affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Sciences, Institute of Software, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences & University of CAS, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058964600","display_name":"Qiuye Wang","orcid":"https://orcid.org/0000-0001-5138-3273"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuye Wang","raw_affiliation_strings":["State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Fermat Labs, Huawei Inc., Dongguan, China","Institute of Software, Chinese Academy of Sciences, China and Huawei Inc., China"],"raw_orcid":"https://orcid.org/0000-0001-5138-3273","affiliations":[{"raw_affiliation_string":"State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Fermat Labs, Huawei Inc., Dongguan, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, China and Huawei Inc., China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai Xue","raw_affiliation_strings":["Key Lab. of System Software and State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","Institute of Software, Chinese Academy of Sciences & University of CAS, China"],"raw_orcid":"https://orcid.org/0000-0001-9717-846X","affiliations":[{"raw_affiliation_string":"Key Lab. of System Software and State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences & University of CAS, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026435847","display_name":"Naijun Zhan","orcid":"https://orcid.org/0000-0003-3298-3817"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naijun Zhan","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technology, School of Computer Science, Peking University, Beijing, China and State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","Peking University, China and Institute of Software, Chinese Academy of Sciences, China"],"raw_orcid":"https://orcid.org/0000-0003-3298-3817","affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technology, School of Computer Science, Peking University, Beijing, China and State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Peking University, China and Institute of Software, Chinese Academy of Sciences, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I20231570","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["Key Lab. of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences & University of CAS, China"],"raw_orcid":"https://orcid.org/0000-0001-9973-2217","affiliations":[{"raw_affiliation_string":"Key Lab. of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210129227"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences & University of CAS, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072831508","display_name":"Zhihong Yang","orcid":"https://orcid.org/0000-0001-9536-1527"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Hong Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, China","Central South University, China"],"raw_orcid":"https://orcid.org/0000-0002-7489-9237","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"Central South University, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100584460"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"],"apc_list":null,"apc_paid":null,"fwci":0.3457,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66583812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"47","issue":"1","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998000264167786,"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":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.996999979019165,"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/computer-science","display_name":"Computer science","score":0.8004573583602905},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7559918165206909},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47225135564804077},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3847315311431885},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35131174325942993},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3372041881084442},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.26495635509490967},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15665343403816223},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07893297076225281}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8004573583602905},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7559918165206909},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47225135564804077},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3847315311431885},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35131174325942993},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3372041881084442},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26495635509490967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15665343403816223},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07893297076225281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3708559","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3708559","pdf_url":null,"source":{"id":"https://openalex.org/S41449414","display_name":"ACM Transactions on Programming Languages and Systems","issn_l":"0164-0925","issn":["0164-0925","1558-4593"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"ACM Transactions on Programming Languages and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1415909970","display_name":null,"funder_award_id":"62192732","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2838552071","display_name":null,"funder_award_id":"2022YFA1005101","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G315913835","display_name":null,"funder_award_id":"12201425","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5423756507","display_name":null,"funder_award_id":"2022YFA1005101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":88,"referenced_works":["https://openalex.org/W79590482","https://openalex.org/W91728630","https://openalex.org/W1480909796","https://openalex.org/W1495570069","https://openalex.org/W1510368738","https://openalex.org/W1558356971","https://openalex.org/W1559197676","https://openalex.org/W1563374593","https://openalex.org/W1565898282","https://openalex.org/W1585981132","https://openalex.org/W1589297860","https://openalex.org/W1592336371","https://openalex.org/W1627251346","https://openalex.org/W1786112247","https://openalex.org/W1792477536","https://openalex.org/W1937324737","https://openalex.org/W1948975400","https://openalex.org/W1964603869","https://openalex.org/W1967344706","https://openalex.org/W1967845657","https://openalex.org/W1970168990","https://openalex.org/W1971043610","https://openalex.org/W1973425711","https://openalex.org/W1978485957","https://openalex.org/W1980450998","https://openalex.org/W1982538489","https://openalex.org/W1995246641","https://openalex.org/W2003141394","https://openalex.org/W2016056788","https://openalex.org/W2016389104","https://openalex.org/W2031373197","https://openalex.org/W2039205672","https://openalex.org/W2046491103","https://openalex.org/W2095551467","https://openalex.org/W2096185905","https://openalex.org/W2099629271","https://openalex.org/W2102696258","https://openalex.org/W2133404041","https://openalex.org/W2136333450","https://openalex.org/W2247845964","https://openalex.org/W2295030121","https://openalex.org/W2398327122","https://openalex.org/W2507512032","https://openalex.org/W2514073783","https://openalex.org/W2522207775","https://openalex.org/W2549857394","https://openalex.org/W2607886860","https://openalex.org/W2761297771","https://openalex.org/W2767382859","https://openalex.org/W2780276625","https://openalex.org/W2781303448","https://openalex.org/W2904362559","https://openalex.org/W2963164018","https://openalex.org/W2987907651","https://openalex.org/W3032926390","https://openalex.org/W3033642953","https://openalex.org/W3033865919","https://openalex.org/W3042261571","https://openalex.org/W3046796804","https://openalex.org/W3099870977","https://openalex.org/W3108376486","https://openalex.org/W3133708012","https://openalex.org/W3167391728","https://openalex.org/W3185235159","https://openalex.org/W4206079487","https://openalex.org/W4206734868","https://openalex.org/W4210577781","https://openalex.org/W4225593432","https://openalex.org/W4225889696","https://openalex.org/W4226455345","https://openalex.org/W4250589301","https://openalex.org/W4251912342","https://openalex.org/W4255442211","https://openalex.org/W4283462359","https://openalex.org/W4293258886","https://openalex.org/W4296691831","https://openalex.org/W4298290503","https://openalex.org/W4299599836","https://openalex.org/W4312519821","https://openalex.org/W4362659518","https://openalex.org/W4366451130","https://openalex.org/W4384155522","https://openalex.org/W4385005490","https://openalex.org/W4385665043","https://openalex.org/W4390603443","https://openalex.org/W4400973450","https://openalex.org/W4402425164","https://openalex.org/W4402496158"],"related_works":["https://openalex.org/W1983756092","https://openalex.org/W2381295697","https://openalex.org/W2385886188","https://openalex.org/W2378309693","https://openalex.org/W579949368","https://openalex.org/W1788812054","https://openalex.org/W2024507128","https://openalex.org/W2288891047","https://openalex.org/W3166939022","https://openalex.org/W2092089517"],"abstract_inverted_index":{"Constraint-solving-based":[0],"program":[1],"invariant":[2,7,13,34,52,102,107,158,168,192],"synthesis":[3,35,53,103,159,169],"takes":[4],"a":[5,43,115,122,145,188],"parametric":[6],"template":[8],"and":[9,73,120,141,201,225],"encodes":[10],"the":[11,21,32,39,50,59,66,100,129,137,152,156,166,174,182,208],"(inductive)":[12],"conditions":[14],"into":[15,212],"constraints.":[16],"The":[17,96,162],"problem":[18,36,40,54,104,170],"of":[19,23,41,88,117,124,128,131,191],"characterizing":[20],"set":[22,130],"all":[24],"valid":[25,45,132],"parameter":[26,46,133],"assignments":[27],"is":[28,48],"referred":[29],"to":[30,217,230],"as":[31],"strong":[33,101],",":[37],"while":[38],"finding":[42],"concrete":[44],"assignment":[47],"called":[49],"weak":[51,142,157,167],".":[55],"For":[56],"both":[57],"problems,":[58],"challenge":[60],"lies":[61],"in":[62,171,233],"solving":[63],"or":[64],"reducing":[65],"encoded":[67],"constraints,":[68],"which":[69],"are":[70],"generally":[71],"non-convex":[72],"lack":[74],"efficient":[75],"solvers.":[76],"In":[77],"this":[78],"article,":[79],"we":[80],"propose":[81],"two":[82],"novel":[83],"algorithms":[84,221],"for":[85,105],"synthesizing":[86],"invariants":[87],"polynomial":[89,106,199],"programs":[90],"using":[91],"semidefinite":[92],"programming":[93],"(SDP):":[94],"(1)":[95],"Cluster":[97,183],"algorithm":[98,164,184,209],"targets":[99],"templates.":[108,150],"Leveraging":[109],"robust":[110],"optimization":[111],"techniques,":[112],"it":[113],"solves":[114],"series":[116],"SDP":[118,218],"relaxations":[119],"yields":[121],"sequence":[123],"increasingly":[125],"precise":[126],"under-approximations":[127],"assignments.":[134],"We":[135],"prove":[136],"algorithm\u2019s":[138],"soundness,":[139],"convergence,":[140],"completeness":[143],"under":[144],"specific":[146,189],"robustness":[147,176],"assumption":[148,177],"on":[149],"Moreover,":[151],"outputs":[153],"can":[154],"simplify":[155],"problem.":[160],"(2)":[161],"Mask":[163],"addresses":[165],"scenarios":[172],"where":[173],"aforementioned":[175],"does":[178],"not":[179],"hold,":[180],"rendering":[181],"ineffective.":[185],"It":[186],"identifies":[187],"subclass":[190],"templates,":[193,196],"termed":[194],"masked":[195],"involving":[197],"parameterized":[198],"equalities":[200],"known":[202],"inequalities.":[203],"By":[204],"applying":[205],"variable":[206],"substitution,":[207],"transforms":[210],"constraints":[211],"an":[213],"equivalent":[214],"form":[215],"amenable":[216],"relaxations.":[219],"Both":[220],"have":[222],"been":[223],"implemented":[224],"demonstrated":[226],"superior":[227],"performance":[228],"compared":[229],"state-of-the-art":[231],"methods":[232],"our":[234],"empirical":[235],"evaluation.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}