{"id":"https://openalex.org/W1948975400","doi":"https://doi.org/10.1007/978-3-319-21690-4_44","title":"Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation","display_name":"Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1948975400","doi":"https://doi.org/10.1007/978-3-319-21690-4_44","mag":"1948975400"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-21690-4_44","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-21690-4_44","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048614307","display_name":"Yu\u2010Fang Chen","orcid":"https://orcid.org/0000-0003-2872-0336"},"institutions":[{"id":"https://openalex.org/I4210098366","display_name":"Institute of Information Science, Academia Sinica","ror":"https://ror.org/00z83z196","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210098366","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Yu-Fang Chen","raw_affiliation_strings":["Institute of Information Science, Academia Sinica, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Science, Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I4210098366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064227560","display_name":"Chih-Duo Hong","orcid":"https://orcid.org/0000-0002-4064-8413"},"institutions":[{"id":"https://openalex.org/I4210098366","display_name":"Institute of Information Science, Academia Sinica","ror":"https://ror.org/00z83z196","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210098366","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chih-Duo Hong","raw_affiliation_strings":["Institute of Information Science, Academia Sinica, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Science, Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I4210098366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023111671","display_name":"Bow-Yaw Wang","orcid":"https://orcid.org/0000-0002-5757-545X"},"institutions":[{"id":"https://openalex.org/I4210098366","display_name":"Institute of Information Science, Academia Sinica","ror":"https://ror.org/00z83z196","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210098366","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Bow-Yaw Wang","raw_affiliation_strings":["Institute of Information Science, Academia Sinica, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Science, Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I4210098366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100448153","display_name":"Lijun Zhang","orcid":"https://orcid.org/0000-0002-3692-2088"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijun Zhang","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China","institution_ids":["https://openalex.org/I4210128818"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048614307"],"corresponding_institution_ids":["https://openalex.org/I4210098366"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.8433,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.84499557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"658","last_page":"674"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9993000030517578,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9771000146865845,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.7577362060546875},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.7405864000320435},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6509688496589661},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5922772288322449},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5666335821151733},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5235076546669006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4964972138404846},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.4938381314277649},{"id":"https://openalex.org/keywords/birkhoff-interpolation","display_name":"Birkhoff interpolation","score":0.49091488122940063},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49079760909080505},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4880160391330719},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.4721118211746216},{"id":"https://openalex.org/keywords/inverse-quadratic-interpolation","display_name":"Inverse quadratic interpolation","score":0.42808863520622253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3890928328037262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36406409740448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3621706962585449},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36017537117004395},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.3395938277244568},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31085145473480225},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15831628441810608},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.15670499205589294},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15137821435928345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10312369465827942}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7577362060546875},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.7405864000320435},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6509688496589661},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5922772288322449},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5666335821151733},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5235076546669006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4964972138404846},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.4938381314277649},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.49091488122940063},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49079760909080505},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4880160391330719},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.4721118211746216},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.42808863520622253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3890928328037262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36406409740448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3621706962585449},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36017537117004395},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3395938277244568},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31085145473480225},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15831628441810608},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.15670499205589294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15137821435928345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10312369465827942},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-21690-4_44","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-21690-4_44","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W57094165","https://openalex.org/W94183712","https://openalex.org/W1480909796","https://openalex.org/W1563374593","https://openalex.org/W1729037535","https://openalex.org/W1734364899","https://openalex.org/W1925669739","https://openalex.org/W1938285999","https://openalex.org/W1986264093","https://openalex.org/W1998777945","https://openalex.org/W2014354084","https://openalex.org/W2024355065","https://openalex.org/W2028981130","https://openalex.org/W2045932400","https://openalex.org/W2069300761","https://openalex.org/W2075498078","https://openalex.org/W2098022036","https://openalex.org/W2098045685","https://openalex.org/W2103953153","https://openalex.org/W2105443791","https://openalex.org/W2111706174","https://openalex.org/W2119029543","https://openalex.org/W2124749403","https://openalex.org/W2136333450","https://openalex.org/W2184410169","https://openalex.org/W2329984281","https://openalex.org/W2751862591","https://openalex.org/W2987907651","https://openalex.org/W3005318059","https://openalex.org/W3146075203","https://openalex.org/W3217399827","https://openalex.org/W4229917934","https://openalex.org/W4235444011","https://openalex.org/W4236478587","https://openalex.org/W4246575101","https://openalex.org/W4251912342"],"related_works":["https://openalex.org/W2354378723","https://openalex.org/W2095809698","https://openalex.org/W4386512906","https://openalex.org/W2488705107","https://openalex.org/W2536408477","https://openalex.org/W2351859300","https://openalex.org/W4200281652","https://openalex.org/W1648644969","https://openalex.org/W2358123980","https://openalex.org/W2387259408"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
