{"id":"https://openalex.org/W1582592616","doi":"https://doi.org/10.1007/978-3-642-02959-2_23","title":"Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic","display_name":"Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1582592616","doi":"https://doi.org/10.1007/978-3-642-02959-2_23","mag":"1582592616"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-02959-2_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-02959-2_23","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/A5069149929","display_name":"Cristina Borralleras","orcid":"https://orcid.org/0000-0002-4667-0953"},"institutions":[{"id":"https://openalex.org/I115304662","display_name":"Universitat de Vic - Universitat Central de Catalunya","ror":"https://ror.org/006zjws59","country_code":"ES","type":"education","lineage":["https://openalex.org/I115304662"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Cristina Borralleras","raw_affiliation_strings":["Universidad de Vic, Spain"],"affiliations":[{"raw_affiliation_string":"Universidad de Vic, Spain","institution_ids":["https://openalex.org/I115304662"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012146310","display_name":"Salvador Lucas","orcid":"https://orcid.org/0000-0001-9923-2108"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Salvador Lucas","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain","Universitat Polit\u00e9cnica de Val\u00e9ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Universitat Polit\u00e9cnica de Val\u00e9ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024291939","display_name":"Rafael Navarro-Marset","orcid":null},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Navarro-Marset","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain","Universitat Polit\u00e9cnica de Val\u00e9ncia, Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Universitat Polit\u00e9cnica de Val\u00e9ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091244452","display_name":"Enric Rodr\u00edguez-Carbonell","orcid":"https://orcid.org/0000-0003-1061-3954"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Enric Rodr\u00edguez-Carbonell","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","Universitat Polit\u00e8cnica de Catalunya, Barcelona  Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya, Barcelona  Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021913033","display_name":"Albert Rubio","orcid":"https://orcid.org/0000-0002-0501-9830"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Albert Rubio","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","Universitat Polit\u00e8cnica de Catalunya, Barcelona  Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya, Barcelona  Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5069149929"],"corresponding_institution_ids":["https://openalex.org/I115304662"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.1978,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9639606,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"294","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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/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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.996999979019165,"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/modulo","display_name":"Modulo","score":0.7396153211593628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6990947723388672},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6362868547439575},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5978302955627441},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.49785852432250977},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.45921561121940613},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4337252080440521},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43035590648651123},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37508460879325867},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3711313009262085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2616274356842041},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24492329359054565}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7396153211593628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6990947723388672},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6362868547439575},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5978302955627441},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.49785852432250977},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45921561121940613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4337252080440521},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43035590648651123},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37508460879325867},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3711313009262085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2616274356842041},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24492329359054565},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-642-02959-2_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-02959-2_23","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.3576","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.3576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dsic.upv.es/~slucas/papers/cade09/cade09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.491.5880","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.491.5880","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lsi.upc.edu/~erodri/webpage/papers/cade09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W91193428","https://openalex.org/W92576581","https://openalex.org/W1480909796","https://openalex.org/W1484559376","https://openalex.org/W1523211942","https://openalex.org/W1533812350","https://openalex.org/W1543075099","https://openalex.org/W1544079619","https://openalex.org/W1556566737","https://openalex.org/W1566656731","https://openalex.org/W1574151794","https://openalex.org/W1583295953","https://openalex.org/W1603813317","https://openalex.org/W1775468415","https://openalex.org/W1978221548","https://openalex.org/W1988455648","https://openalex.org/W2003804739","https://openalex.org/W2090855107","https://openalex.org/W2125967324","https://openalex.org/W2149605327","https://openalex.org/W2163850966","https://openalex.org/W2164290630","https://openalex.org/W2406142175","https://openalex.org/W2612793397","https://openalex.org/W2798401172","https://openalex.org/W2911880377"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2097470475","https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W2941201715","https://openalex.org/W2025727968","https://openalex.org/W238211858","https://openalex.org/W4297742300","https://openalex.org/W1774334694","https://openalex.org/W2099799091"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}