{"id":"https://openalex.org/W1836569189","doi":"https://doi.org/10.1007/978-3-540-31954-2_35","title":"Primal\u2013Dual Tests for Safety and Reachability","display_name":"Primal\u2013Dual Tests for Safety and Reachability","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1836569189","doi":"https://doi.org/10.1007/978-3-540-31954-2_35","mag":"1836569189"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-31954-2_35","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-31954-2_35","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/A5022400557","display_name":"S. Prajna","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen Prajna","raw_affiliation_strings":["Control and Dynamical Systems, California Institute of Technology, Pasadena, USA","Control and Dynamical Systems, California Institute of Technology, Pasadena, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Control and Dynamical Systems, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Control and Dynamical Systems, California Institute of Technology, Pasadena, CA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091667471","display_name":"Anders Rantzer","orcid":"https://orcid.org/0000-0001-7118-2786"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anders Rantzer","raw_affiliation_strings":["Department of Automatic Control, Lund Institute of Technology, Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund Institute of Technology, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":4.1643,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.94757885,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"542","last_page":"556"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9980999827384949,"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":0.9980999827384949,"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/T11357","display_name":"Risk and Safety Analysis","score":0.9563000202178955,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.920199990272522,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9481295347213745},{"id":"https://openalex.org/keywords/certificate","display_name":"Certificate","score":0.6600435972213745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6406657099723816},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5423821210861206},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5146001577377319},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5012145042419434},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4935034513473511},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.48960787057876587},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4822302758693695},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4342612028121948},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2823028564453125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2667592763900757},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17015838623046875},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15440335869789124}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9481295347213745},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.6600435972213745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6406657099723816},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5423821210861206},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5146001577377319},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5012145042419434},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4935034513473511},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.48960787057876587},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4822302758693695},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4342612028121948},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2823028564453125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2667592763900757},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17015838623046875},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15440335869789124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-31954-2_35","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-31954-2_35","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":34,"referenced_works":["https://openalex.org/W1506588809","https://openalex.org/W1522448884","https://openalex.org/W1530240157","https://openalex.org/W1540897666","https://openalex.org/W1568518466","https://openalex.org/W1569146343","https://openalex.org/W1582811927","https://openalex.org/W1585526574","https://openalex.org/W1607353007","https://openalex.org/W1726255445","https://openalex.org/W1729334489","https://openalex.org/W1897764801","https://openalex.org/W1994475353","https://openalex.org/W2045938917","https://openalex.org/W2053913299","https://openalex.org/W2069323107","https://openalex.org/W2077367989","https://openalex.org/W2093916942","https://openalex.org/W2099354898","https://openalex.org/W2102696258","https://openalex.org/W2106850246","https://openalex.org/W2112407936","https://openalex.org/W2117218135","https://openalex.org/W2125369458","https://openalex.org/W2126749600","https://openalex.org/W2131441094","https://openalex.org/W2133404041","https://openalex.org/W2156301326","https://openalex.org/W2296319761","https://openalex.org/W2340735175","https://openalex.org/W2561675875","https://openalex.org/W2612952478","https://openalex.org/W2913459036","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W2127267268","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2156446763","https://openalex.org/W2143461633","https://openalex.org/W2150194458","https://openalex.org/W4321471459","https://openalex.org/W2889071233","https://openalex.org/W2000285254","https://openalex.org/W3153752017"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}