{"id":"https://openalex.org/W3046796804","doi":"https://doi.org/10.1007/978-3-030-53288-8_20","title":"Nonlinear Craig Interpolant Generation","display_name":"Nonlinear Craig Interpolant Generation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3046796804","doi":"https://doi.org/10.1007/978-3-030-53288-8_20","mag":"3046796804"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-53288-8_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-53288-8_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-53288-8_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-53288-8_20.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101885727","display_name":"Ting Gan","orcid":"https://orcid.org/0000-0002-4880-5129"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Gan","raw_affiliation_strings":["School of Computer Science, Wuhan University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-4880-5129","affiliations":[{"raw_affiliation_string":"School of Computer Science, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065639971","display_name":"Bican Xia","orcid":"https://orcid.org/0000-0002-2570-2338"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bican Xia","raw_affiliation_strings":["LMAM, School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-2570-2338","affiliations":[{"raw_affiliation_string":"LMAM, School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"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/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"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai Xue","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-9717-846X","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"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/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"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naijun Zhan","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-3298-3817","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102749961","display_name":"Liyun Dai","orcid":"https://orcid.org/0000-0002-2615-9381"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liyun Dai","raw_affiliation_strings":["RISE, School of Computer and Information Science, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-2615-9381","affiliations":[{"raw_affiliation_string":"RISE, School of Computer and Information Science, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5065639971"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":3.6175,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.9334004,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"415","last_page":"438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9973999857902527,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9962000250816345,"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/wedge","display_name":"Wedge (geometry)","score":0.5773876309394836},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5088241696357727},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5049100518226624},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48409807682037354},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4794789254665375},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4762002229690552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45251843333244324},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4190010130405426},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3858048617839813},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.372081995010376},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35013097524642944},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31615811586380005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2704775929450989},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20544716715812683},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1718275249004364},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1543436050415039},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12373286485671997},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07590615749359131}],"concepts":[{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.5773876309394836},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5088241696357727},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5049100518226624},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48409807682037354},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4794789254665375},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4762002229690552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45251843333244324},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4190010130405426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3858048617839813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.372081995010376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35013097524642944},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31615811586380005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2704775929450989},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20544716715812683},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1718275249004364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1543436050415039},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12373286485671997},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07590615749359131},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-030-53288-8_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-53288-8_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-53288-8_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pubmedcentral.nih.gov:7363235","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7363235","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Aided Verification","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-53288-8_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-53288-8_20","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-53288-8_20.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3291759789","display_name":"\u9762\u5411\u7a0b\u5e8f\u9a8c\u8bc1\u7684\u81ea\u52a8\u5b9a\u7406\u8bc1\u660e\u7406\u8bba\u3001\u65b9\u6cd5\u4e0e\u5de5\u5177\u7814\u7a76","funder_award_id":"61732001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5315938056","display_name":null,"funder_award_id":"61902284","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5543570208","display_name":null,"funder_award_id":"61625206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7097245526","display_name":"\u7c7b\u4eba\u4efb\u52a1\u89c4\u5212\u3001\u63a8\u7406\u53ca\u5176\u9a8c\u8bc1\u7cfb\u7edf\u7684\u7814\u7a76\u548c\u5e94\u7528","funder_award_id":"61836005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7468986614","display_name":"\u5927\u89c4\u6a21\u6982\u7387\u5e76\u53d1\u5b9e\u65f6\u7cfb\u7edf\u6a21\u578b\u68c0\u9a8c","funder_award_id":"61532019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8157162002","display_name":null,"funder_award_id":"61802318","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3046796804.pdf","grobid_xml":"https://content.openalex.org/works/W3046796804.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W207011911","https://openalex.org/W1497571013","https://openalex.org/W1499948164","https://openalex.org/W1510368738","https://openalex.org/W1515795741","https://openalex.org/W1516304047","https://openalex.org/W1517192598","https://openalex.org/W1539838732","https://openalex.org/W1592751003","https://openalex.org/W1609596465","https://openalex.org/W1790432088","https://openalex.org/W1792477536","https://openalex.org/W1986264093","https://openalex.org/W1999613943","https://openalex.org/W2038334086","https://openalex.org/W2044095368","https://openalex.org/W2044632231","https://openalex.org/W2080803951","https://openalex.org/W2080841971","https://openalex.org/W2084294613","https://openalex.org/W2085352155","https://openalex.org/W2099316895","https://openalex.org/W2108174021","https://openalex.org/W2151463894","https://openalex.org/W2243684585","https://openalex.org/W2295030121","https://openalex.org/W2475413394","https://openalex.org/W2536620281","https://openalex.org/W2565511473","https://openalex.org/W2761297771","https://openalex.org/W2767382859","https://openalex.org/W2913808178","https://openalex.org/W2918985823","https://openalex.org/W2963067774","https://openalex.org/W2963601994","https://openalex.org/W2969437902","https://openalex.org/W3101234909","https://openalex.org/W4234184051","https://openalex.org/W4254377784","https://openalex.org/W4254838945","https://openalex.org/W4255442211","https://openalex.org/W4293258886","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W2017385525","https://openalex.org/W2042698599","https://openalex.org/W1999187231","https://openalex.org/W4248634293","https://openalex.org/W2351605363","https://openalex.org/W2090638913","https://openalex.org/W2358303194","https://openalex.org/W2089136900","https://openalex.org/W2072315057","https://openalex.org/W1895124089"],"abstract_inverted_index":{"Craig":[0],"interpolant":[1,45,106,133],"generation":[2,171],"for":[3,52],"non-linear":[4,31],"theory":[5],"and":[6,27,62,91,134],"its":[7],"combination":[8],"with":[9,68],"other":[10],"theories":[11],"are":[12,33,80],"still":[13],"in":[14,22,82,143,172],"infancy,":[15],"although":[16],"interpolation-based":[17],"techniques":[18],"have":[19],"become":[20],"popular":[21],"the":[23,47,69,92,128,131,137],"verification":[24,124],"of":[25,46,130],"programs":[26],"hybrid":[28],"systems":[29],"where":[30,78],"expressions":[32],"very":[34],"common.":[35],"In":[36,119],"this":[37],"paper,":[38],"we":[39,101,121,147,162],"first":[40],"prove":[41],"that":[42,103],"a":[43,112,123],"polynomial":[44,56],"form":[48,70],"$$h(\\mathbf":[49],"{x})>0$$":[50],"exists":[51],"two":[53],"mutually":[54],"contradictory":[55],"formulas":[57],"$$\\phi":[58],"(\\mathbf":[59,64],"{x},\\mathbf":[60,65,84,88],"{y})$$":[61],"$$\\psi":[63],"{z})$$":[66],",":[67,77,90],"$$f_1\\ge":[71],"0\\wedge":[72],"\\cdots":[73],"\\wedge":[74],"f_n\\ge":[75],"0$$":[76],"$$f_i$$":[79,97],"polynomials":[81],"$$\\mathbf":[83,87],"{y}$$":[85],"or":[86],"{z}$$":[89],"quadratic":[93],"module":[94],"generated":[95],"by":[96,140],"is":[98],"Archimedean.":[99],"Then,":[100],"show":[102],"synthesizing":[104],"such":[105],"can":[107],"be":[108],"reduced":[109],"to":[110,126,150,154,165,169],"solving":[111],"semi-definite":[113],"programming":[114],"problem":[115],"(":[116],"$$\\mathrm{SDP}$$":[117,144],").":[118],"addition,":[120],"propose":[122],"approach":[125,153,168],"assure":[127],"validity":[129],"synthesized":[132],"consequently":[135],"avoid":[136],"unsoundness":[138],"caused":[139],"numerical":[141],"error":[142],"solving.":[145],"Besides,":[146],"discuss":[148],"how":[149,164],"generalize":[151],"our":[152,167],"general":[155],"semi-algebraic":[156],"formulas.":[157],"Finally,":[158],"as":[159],"an":[160],"application,":[161],"demonstrate":[163],"apply":[166],"invariant":[170],"program":[173],"verification.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}