{"id":"https://openalex.org/W2087749124","doi":"https://doi.org/10.1007/s10703-007-0046-1","title":"Constructing invariants for hybrid systems","display_name":"Constructing invariants for hybrid systems","publication_year":2007,"publication_date":"2007-12-05","ids":{"openalex":"https://openalex.org/W2087749124","doi":"https://doi.org/10.1007/s10703-007-0046-1","mag":"2087749124"},"language":"en","primary_location":{"id":"doi:10.1007/s10703-007-0046-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10703-007-0046-1","pdf_url":null,"source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","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/A5103106502","display_name":"Sriram Sankaranarayanan","orcid":"https://orcid.org/0000-0001-7315-4340"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sriram Sankaranarayanan","raw_affiliation_strings":["Computer Science Department, Stanford University, Stanford, CA, 94305, USA","Computer Science Department, Stanford University, Stanford, USA 94305"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, CA, 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, USA 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058348937","display_name":"Henny B. Sipma","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henny B. Sipma","raw_affiliation_strings":["Computer Science Department, Stanford University, Stanford, CA, 94305, USA","Computer Science Department, Stanford University, Stanford, USA 94305"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, CA, 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, USA 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034436241","display_name":"Zohar Manna","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zohar Manna","raw_affiliation_strings":["Computer Science Department, Stanford University, Stanford, CA, 94305, USA","Computer Science Department, Stanford University, Stanford, USA 94305"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, CA, 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, USA 94305","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103106502"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3490},"apc_paid":null,"fwci":6.7379,"has_fulltext":false,"cited_by_count":122,"citation_normalized_percentile":{"value":0.97025888,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"32","issue":"1","first_page":"25","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9957000017166138,"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":0.9872000217437744,"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/invariant","display_name":"Invariant (physics)","score":0.736507773399353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6303456425666809},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"Invariant theory","score":0.5845115780830383},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5284801721572876},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5249630808830261},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46138718724250793},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4513694941997528},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3657090663909912},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3477397561073303},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1061575710773468}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.736507773399353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6303456425666809},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.5845115780830383},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5284801721572876},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5249630808830261},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46138718724250793},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4513694941997528},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3657090663909912},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3477397561073303},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1061575710773468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10703-007-0046-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10703-007-0046-1","pdf_url":null,"source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.2632","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.2632","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~sipma/papers/hscc04.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.124.2004","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.2004","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~srirams/papers/hscc04.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.124.5820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~srirams/papers/differential.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.125.309","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~srirams/papers/hscc04.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.9979","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.9979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/~sipma/papers/hscc04.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W120333500","https://openalex.org/W132366648","https://openalex.org/W1483379332","https://openalex.org/W1495570069","https://openalex.org/W1502028089","https://openalex.org/W1518341038","https://openalex.org/W1540180001","https://openalex.org/W1543209374","https://openalex.org/W1554063378","https://openalex.org/W1563374593","https://openalex.org/W1568518466","https://openalex.org/W1583295953","https://openalex.org/W1585526574","https://openalex.org/W1589297860","https://openalex.org/W1596664612","https://openalex.org/W1599897266","https://openalex.org/W1603048013","https://openalex.org/W1607353007","https://openalex.org/W1684406198","https://openalex.org/W1967184028","https://openalex.org/W1967845657","https://openalex.org/W1986264093","https://openalex.org/W1994475353","https://openalex.org/W1996109622","https://openalex.org/W2007074311","https://openalex.org/W2011039300","https://openalex.org/W2023499821","https://openalex.org/W2031373197","https://openalex.org/W2043100293","https://openalex.org/W2063685460","https://openalex.org/W2096035734","https://openalex.org/W2098045685","https://openalex.org/W2112407936","https://openalex.org/W2132661148","https://openalex.org/W2147340401","https://openalex.org/W2160883697","https://openalex.org/W2165276844","https://openalex.org/W2476096155","https://openalex.org/W4229571709","https://openalex.org/W4230919050","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2088544526","https://openalex.org/W4296940695","https://openalex.org/W2950568206","https://openalex.org/W4377158067","https://openalex.org/W2951029692","https://openalex.org/W2615709397","https://openalex.org/W163171588","https://openalex.org/W4382173277","https://openalex.org/W2963092292","https://openalex.org/W4297699348"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
