{"id":"https://openalex.org/W2002298564","doi":"https://doi.org/10.1007/s11334-012-0189-0","title":"Invariant relations, invariant functions, and loop functions","display_name":"Invariant relations, invariant functions, and loop functions","publication_year":2012,"publication_date":"2012-08-13","ids":{"openalex":"https://openalex.org/W2002298564","doi":"https://doi.org/10.1007/s11334-012-0189-0","mag":"2002298564"},"language":"en","primary_location":{"id":"doi:10.1007/s11334-012-0189-0","doi":"https://doi.org/10.1007/s11334-012-0189-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11334-012-0189-0","pdf_url":null,"source":{"id":"https://openalex.org/S151239915","display_name":"Innovations in Systems and Software Engineering","issn_l":"1614-5046","issn":["1614-5046","1614-5054"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-3"],"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":"Innovations in Systems and Software Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5006442971","display_name":"Lamia Labed Jilani","orcid":"https://orcid.org/0000-0001-7842-0185","observed_orcids":["https://orcid.org/0000-0001-7842-0185"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lamia Labed Jilani","raw_affiliation_strings":["Institut Sup de Gestion, 2000, Bardo, Tunisia","Institut Sup de Gestion, Bardo, Tunisia 2000#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Sup de Gestion, 2000, Bardo, Tunisia","institution_ids":[]},{"raw_affiliation_string":"Institut Sup de Gestion, Bardo, Tunisia 2000#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032654524","display_name":"Asma Louhichi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Asma Louhichi","raw_affiliation_strings":["Institut Sup d\u2019Inform. et Multimedia, 2080, Ariana, Tunisia","Institut Sup d'Inform. et Multimedia, Ariana, Tunisia 2080#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Sup d\u2019Inform. et Multimedia, 2080, Ariana, Tunisia","institution_ids":[]},{"raw_affiliation_string":"Institut Sup d'Inform. et Multimedia, Ariana, Tunisia 2080#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066229458","display_name":"Olfa Mraihi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olfa Mraihi","raw_affiliation_strings":["Institut Sup de Gestion, 2000, Bardo, Tunisia","Institut Sup de Gestion, Bardo, Tunisia 2000#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Sup de Gestion, 2000, Bardo, Tunisia","institution_ids":[]},{"raw_affiliation_string":"Institut Sup de Gestion, Bardo, Tunisia 2000#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115598651","display_name":"Ali Mili","orcid":"https://orcid.org/0000-0002-6578-5510","observed_orcids":["https://orcid.org/0000-0002-6578-5510"]},"institutions":[{"id":"https://openalex.org/I118118575","display_name":"New Jersey Institute of Technology","ror":"https://ror.org/05e74xb87","country_code":"US","type":"education","lineage":["https://openalex.org/I118118575"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Mili","raw_affiliation_strings":["CCS, NJIT, Newark, NJ, 07102, USA","CCS, NJIT, Newark, USA 07102"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CCS, NJIT, Newark, NJ, 07102, USA","institution_ids":["https://openalex.org/I118118575"]},{"raw_affiliation_string":"CCS, NJIT, Newark, USA 07102","institution_ids":["https://openalex.org/I118118575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006442971"],"corresponding_institution_ids":[],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.6169,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73729461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":95},"biblio":{"volume":"8","issue":"3","first_page":"195","last_page":"212"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8008000254631042,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8008000254631042,"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"}},{"id":"https://openalex.org/T10260","display_name":"Software Engineering Research","score":0.17149999737739563,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.004800000227987766,"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/invariant-relations","display_name":"invariant relations","score":0.9049999713897705},{"id":"https://openalex.org/keywords/invariant-functions","display_name":"invariant functions","score":0.9580000042915344},{"id":"https://openalex.org/keywords/loop-functions","display_name":"loop functions","score":0.9869999885559082},{"id":"https://openalex.org/keywords/while-loops","display_name":"while loops","score":0.7319999933242798},{"id":"https://openalex.org/keywords/theory-of-relations","display_name":"theory of relations","score":0.6819999814033508},{"id":"https://openalex.org/keywords/program-analysis","display_name":"program analysis","score":0.7990000247955322},{"id":"https://openalex.org/keywords/program-comprehension","display_name":"program comprehension","score":0.7279999852180481},{"id":"https://openalex.org/keywords/reverse-engineering","display_name":"reverse engineering","score":0.9240000247955322},{"id":"https://openalex.org/keywords/program-verification","display_name":"program verification","score":0.9919999837875366},{"id":"https://openalex.org/keywords/software-maintenance","display_name":"software maintenance","score":0.8939999938011169}],"concepts":[{"id":"https://openalex.org/C2778514511","wikidata":"https://www.wikidata.org/wiki/Q1374194","display_name":"Programmer","level":2,"score":0.686540424823761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6586518287658691},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.574840247631073},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5330286026000977},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.5115845799446106},{"id":"https://openalex.org/C186846655","wikidata":"https://www.wikidata.org/wiki/Q3398377","display_name":"Software construction","level":4,"score":0.47234880924224854},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.46425917744636536},{"id":"https://openalex.org/C2777561058","wikidata":"https://www.wikidata.org/wiki/Q2652119","display_name":"Program comprehension","level":4,"score":0.46318766474723816},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44815975427627563},{"id":"https://openalex.org/C529173508","wikidata":"https://www.wikidata.org/wiki/Q638608","display_name":"Software development","level":3,"score":0.42803820967674255},{"id":"https://openalex.org/C149091818","wikidata":"https://www.wikidata.org/wiki/Q2429814","display_name":"Software system","level":3,"score":0.36082923412323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14557617902755737},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11334-012-0189-0","doi":"https://doi.org/10.1007/s11334-012-0189-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11334-012-0189-0","pdf_url":null,"source":{"id":"https://openalex.org/S151239915","display_name":"Innovations in Systems and Software Engineering","issn_l":"1614-5046","issn":["1614-5046","1614-5054"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-3"],"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":"Innovations in Systems and Software Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W7737961","https://openalex.org/W148396834","https://openalex.org/W281821942","https://openalex.org/W1535535292","https://openalex.org/W1561089540","https://openalex.org/W1563374593","https://openalex.org/W1661099014","https://openalex.org/W1802373871","https://openalex.org/W1837593827","https://openalex.org/W1923291441","https://openalex.org/W1981525483","https://openalex.org/W2006824750","https://openalex.org/W2007225061","https://openalex.org/W2012895643","https://openalex.org/W2017486666","https://openalex.org/W2031373197","https://openalex.org/W2043100293","https://openalex.org/W2049413589","https://openalex.org/W2062764376","https://openalex.org/W2074592031","https://openalex.org/W2098045685","https://openalex.org/W2099737764","https://openalex.org/W2103299454","https://openalex.org/W2103953153","https://openalex.org/W2106661290","https://openalex.org/W2110908283","https://openalex.org/W2111706174","https://openalex.org/W2113047249","https://openalex.org/W2115223441","https://openalex.org/W2118362509","https://openalex.org/W2131361093","https://openalex.org/W2132251441","https://openalex.org/W2132661148","https://openalex.org/W2134630546","https://openalex.org/W2147543351","https://openalex.org/W2150170258","https://openalex.org/W2293708017","https://openalex.org/W2591438211","https://openalex.org/W2798271294","https://openalex.org/W2987907651","https://openalex.org/W3146075203","https://openalex.org/W4248689402","https://openalex.org/W6960029988"],"related_works":["https://openalex.org/W1870454295","https://openalex.org/W2118456460","https://openalex.org/W4387559288","https://openalex.org/W1981525483","https://openalex.org/W2049413589","https://openalex.org/W2006824750","https://openalex.org/W3140179668","https://openalex.org/W2163049066","https://openalex.org/W7095212309","https://openalex.org/W1995957753"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}