{"id":"https://openalex.org/W1997553387","doi":"https://doi.org/10.1007/s00165-012-0252-5","title":"Proving termination of nonlinear command sequences","display_name":"Proving termination of nonlinear command sequences","publication_year":2012,"publication_date":"2012-06-27","ids":{"openalex":"https://openalex.org/W1997553387","doi":"https://doi.org/10.1007/s00165-012-0252-5","mag":"1997553387"},"language":"en","primary_location":{"id":"doi:10.1007/s00165-012-0252-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00165-012-0252-5","pdf_url":"https://dl.acm.org/doi/pdf/10.1007/s00165-012-0252-5","source":{"id":"https://openalex.org/S128250343","display_name":"Formal Aspects of Computing","issn_l":"0934-5043","issn":["0934-5043","1433-299X"],"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 Aspects of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1007/s00165-012-0252-5","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000765311","display_name":"Domagoj Babi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Domagoj Babi\u0107","raw_affiliation_strings":["Computer Science Division, University of California, Berkeley, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, Berkeley, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112528389","display_name":"Byron Cook","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Byron Cook","raw_affiliation_strings":["Microsoft Research and University College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research and University College London, London, UK","institution_ids":["https://openalex.org/I4210164937","https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050411743","display_name":"Alan J. Hu","orcid":"https://orcid.org/0000-0002-4276-0169"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alan J. Hu","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021217615","display_name":"Zvonimir Rakamari\u0107","orcid":"https://orcid.org/0000-0001-7946-0162"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zvonimir Rakamari\u0107","raw_affiliation_strings":["School of Computing, The University of Utah, Salt Lake City, USA","School of Computing, The University of Utah, Salt Lake City, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, The University of Utah, Salt Lake City, USA","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"School of Computing, The University of Utah, Salt Lake City, USA#TAB#","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7365,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84035148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"25","issue":"3","first_page":"389","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10126","display_name":"Logic, programming, and type systems","score":0.9988999962806702,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9940000176429749,"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/theory-of-computation","display_name":"Theory of computation","score":0.8102649450302124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.716347873210907},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6468415260314941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5581950545310974},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5492761135101318},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5447807908058167},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5396251082420349},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.4726506769657135},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.41557157039642334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3640144467353821},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33107900619506836},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1320303976535797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08085870742797852},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07444790005683899}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.8102649450302124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.716347873210907},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6468415260314941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5581950545310974},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5492761135101318},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5447807908058167},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5396251082420349},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.4726506769657135},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.41557157039642334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3640144467353821},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33107900619506836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1320303976535797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08085870742797852},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07444790005683899},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00165-012-0252-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00165-012-0252-5","pdf_url":"https://dl.acm.org/doi/pdf/10.1007/s00165-012-0252-5","source":{"id":"https://openalex.org/S128250343","display_name":"Formal Aspects of Computing","issn_l":"0934-5043","issn":["0934-5043","1433-299X"],"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 Aspects of Computing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1490855","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1490855/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   FORMAL ASPECTS OF COMPUTING , 25  (3)   pp. 389-403.   (2013)      ","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00165-012-0252-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00165-012-0252-5","pdf_url":"https://dl.acm.org/doi/pdf/10.1007/s00165-012-0252-5","source":{"id":"https://openalex.org/S128250343","display_name":"Formal Aspects of Computing","issn_l":"0934-5043","issn":["0934-5043","1433-299X"],"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 Aspects of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997553387.pdf","grobid_xml":"https://content.openalex.org/works/W1997553387.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W303139982","https://openalex.org/W1503537039","https://openalex.org/W1506323687","https://openalex.org/W1521232193","https://openalex.org/W1530375435","https://openalex.org/W1541144457","https://openalex.org/W1575308494","https://openalex.org/W1575647584","https://openalex.org/W1584357601","https://openalex.org/W1585194019","https://openalex.org/W1593745409","https://openalex.org/W1723067587","https://openalex.org/W1741606568","https://openalex.org/W1899458625","https://openalex.org/W1982205631","https://openalex.org/W1993129359","https://openalex.org/W1996679397","https://openalex.org/W2043100293","https://openalex.org/W2069300761","https://openalex.org/W2098347737","https://openalex.org/W2099949759","https://openalex.org/W2111706174","https://openalex.org/W2114067856","https://openalex.org/W2121365859","https://openalex.org/W2124909257","https://openalex.org/W2135331739","https://openalex.org/W2136333450","https://openalex.org/W2141040012","https://openalex.org/W2153144732","https://openalex.org/W2487992810","https://openalex.org/W2987907651","https://openalex.org/W3146075203","https://openalex.org/W4233310630","https://openalex.org/W4251912342","https://openalex.org/W4285719527","https://openalex.org/W6610773549"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W24774503","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2014821076","https://openalex.org/W3208095355","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W3101625811","https://openalex.org/W2165950148"],"abstract_inverted_index":{"Abstract":[0],"We":[1,57],"describe":[2,59],"a":[3,13,60,70],"simple":[4],"and":[5],"efficient":[6],"algorithm":[7],"for":[8,29,62],"proving":[9,67,73],"the":[10,33,36,46],"termination":[11,47,66,72],"of":[12,15,35,48],"class":[14],"loops":[16,49],"with":[17],"nonlinear":[18,65],"assignments":[19],"to":[20,43],"variables.":[21],"The":[22,39],"method":[23,61],"is":[24],"based":[25],"on":[26,77],"divergence":[27],"testing":[28],"each":[30],"variable":[31],"in":[32],"cone-of-influence":[34],"loop\u2019s":[37],"condition.":[38],"analysis":[40],"allows":[41],"us":[42],"automatically":[44],"prove":[45],"that":[50,75],"cannot":[51],"be":[52],"handled":[53],"using":[54],"previous":[55],"techniques.":[56],"also":[58],"integrating":[63],"our":[64],"technique":[68],"into":[69],"larger":[71],"framework":[74],"depends":[76],"linear":[78],"reasoning.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
