{"id":"https://openalex.org/W2046877387","doi":"https://doi.org/10.1145/2362389.2362390","title":"Equivalence checking of static affine programs using widening to handle recurrences","display_name":"Equivalence checking of static affine programs using widening to handle recurrences","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2046877387","doi":"https://doi.org/10.1145/2362389.2362390","mag":"2046877387"},"language":"en","primary_location":{"id":"doi:10.1145/2362389.2362390","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2362389.2362390","pdf_url":null,"source":{"id":"https://openalex.org/S41449414","display_name":"ACM Transactions on Programming Languages and Systems","issn_l":"0164-0925","issn":["0164-0925","1558-4593"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Programming Languages and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/359595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055650706","display_name":"Sven Verdoolaege","orcid":"https://orcid.org/0000-0003-3179-2736"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Sven Verdoolaege","raw_affiliation_strings":["Katholieke Universiteit Leuven, Belgium","Katholieke Universiteit , Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit , Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084545304","display_name":"Gerda Janssens","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Gerda Janssens","raw_affiliation_strings":["Katholieke Universiteit Leuven, Belgium","Katholieke Universiteit , Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit , Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004343076","display_name":"Maurice Bruynooghe","orcid":"https://orcid.org/0000-0002-6881-1462"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Maurice Bruynooghe","raw_affiliation_strings":["Katholieke Universiteit Leuven, Belgium","Katholieke Universiteit , Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit , Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055650706"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":5.9938,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.96135512,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"1","last_page":"35"},"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":0.9995999932289124,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/computer-science","display_name":"Computer science","score":0.8133820295333862},{"id":"https://openalex.org/keywords/transitive-closure","display_name":"Transitive closure","score":0.7782588005065918},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7534698247909546},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.72889244556427},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6991033554077148},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6920957565307617},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6050624847412109},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4975889027118683},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.4225616455078125},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41956737637519836},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.40447598695755005},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3690881133079529},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16531279683113098},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14474308490753174}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8133820295333862},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.7782588005065918},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7534698247909546},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.72889244556427},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6991033554077148},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6920957565307617},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6050624847412109},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4975889027118683},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.4225616455078125},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41956737637519836},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.40447598695755005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3690881133079529},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16531279683113098},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14474308490753174},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2362389.2362390","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2362389.2362390","pdf_url":null,"source":{"id":"https://openalex.org/S41449414","display_name":"ACM Transactions on Programming Languages and Systems","issn_l":"0164-0925","issn":["0164-0925","1558-4593"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Programming Languages and Systems","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/359595","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/359595","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ACM Transactions on Programming Languages and Systems, vol. 34 (3), Art.No. 11","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/359595","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/359595","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ACM Transactions on Programming Languages and Systems, vol. 34 (3), Art.No. 11","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3716882960","display_name":null,"funder_award_id":"G.0232.06N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W47386445","https://openalex.org/W104652941","https://openalex.org/W1154056748","https://openalex.org/W1480811645","https://openalex.org/W1491410022","https://openalex.org/W1504751168","https://openalex.org/W1510196500","https://openalex.org/W1517343420","https://openalex.org/W1540893634","https://openalex.org/W1541631323","https://openalex.org/W1558370006","https://openalex.org/W1559283829","https://openalex.org/W1568478782","https://openalex.org/W1582651107","https://openalex.org/W1597068544","https://openalex.org/W1802524876","https://openalex.org/W2006508316","https://openalex.org/W2008398511","https://openalex.org/W2013981372","https://openalex.org/W2015478888","https://openalex.org/W2031373197","https://openalex.org/W2032391783","https://openalex.org/W2039222548","https://openalex.org/W2040856861","https://openalex.org/W2040863504","https://openalex.org/W2050948770","https://openalex.org/W2052356107","https://openalex.org/W2102757390","https://openalex.org/W2122767591","https://openalex.org/W2133857440","https://openalex.org/W2134087751","https://openalex.org/W2140311411","https://openalex.org/W2145175129","https://openalex.org/W2151828216","https://openalex.org/W2164162683","https://openalex.org/W2171834078","https://openalex.org/W2202520356","https://openalex.org/W2207131995","https://openalex.org/W2293092623","https://openalex.org/W2294743625","https://openalex.org/W2336662920","https://openalex.org/W2340604309","https://openalex.org/W2506054026","https://openalex.org/W2521316295","https://openalex.org/W2605317797","https://openalex.org/W3087458664","https://openalex.org/W3123589846","https://openalex.org/W3203568064","https://openalex.org/W4210409048","https://openalex.org/W4242965270","https://openalex.org/W4251192040","https://openalex.org/W4253178675","https://openalex.org/W4300934094"],"related_works":["https://openalex.org/W1553139688","https://openalex.org/W2371151875","https://openalex.org/W2136009070","https://openalex.org/W2362009423","https://openalex.org/W2391133415","https://openalex.org/W2012063573","https://openalex.org/W1982015164","https://openalex.org/W203725150","https://openalex.org/W4230967508","https://openalex.org/W1499233953"],"abstract_inverted_index":{"Designers":[0],"often":[1],"apply":[2],"manual":[3],"or":[4],"semi-automatic":[5],"loop":[6],"and":[7,12,57,91],"data":[8],"transformations":[9,23],"on":[10,52,63],"array-":[11],"loop-intensive":[13],"programs":[14],"to":[15,65,98],"improve":[16],"performance.":[17],"It":[18],"is":[19,50,88,92],"crucial":[20],"that":[21],"such":[22],"preserve":[24],"the":[25,28,41,67,93],"functionality":[26],"of":[27,43,95],"program.":[29],"This":[30],"article":[31],"presents":[32],"an":[33],"automatic":[34],"method":[35],"for":[36,40,71],"constructing":[37],"equivalence":[38,48],"proofs":[39],"class":[42],"static":[44],"affine":[45],"programs.":[46],"The":[47,86],"checking":[49],"performed":[51],"a":[53,59],"dependence":[54],"graph":[55],"abstraction":[56],"uses":[58],"new":[60],"approach":[61,80],"based":[62],"widening":[64,79],"find":[66],"proper":[68],"induction":[69],"hypotheses":[70],"reasoning":[72],"about":[73],"recurrences.":[74,85],"Unlike":[75],"transitive-closure-based":[76],"approaches,":[77],"this":[78],"can":[81],"also":[82],"handle":[83],"nonuniform":[84],"implementation":[87],"publicly":[89],"available":[90],"first":[94],"its":[96],"kind":[97],"fully":[99],"support":[100],"commutative":[101],"operations.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}