{"id":"https://openalex.org/W2949888985","doi":"https://doi.org/10.1017/s0960129520000195","title":"Forward analysis for WSTS, part I: completions","display_name":"Forward analysis for WSTS, part I: completions","publication_year":2020,"publication_date":"2020-08-01","ids":{"openalex":"https://openalex.org/W2949888985","doi":"https://doi.org/10.1017/s0960129520000195","mag":"2949888985"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129520000195","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129520000195","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0902.1587v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alain Finkel","orcid":"https://orcid.org/0000-0003-0702-3232"},"institutions":[{"id":"https://openalex.org/I4210104198","display_name":"Laboratoire Sp\u00e9cification et V\u00e9rification","ror":"https://ror.org/01kz1bj67","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210104198","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alain Finkel","raw_affiliation_strings":["LSV"],"raw_orcid":"https://orcid.org/0000-0003-0702-3232","affiliations":[{"raw_affiliation_string":"LSV","institution_ids":["https://openalex.org/I4210104198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032396554","display_name":"Jean Goubault-Larrecq","orcid":"https://orcid.org/0000-0001-5879-3304"},"institutions":[{"id":"https://openalex.org/I4210104198","display_name":"Laboratoire Sp\u00e9cification et V\u00e9rification","ror":"https://ror.org/01kz1bj67","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210104198","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean Goubault-Larrecq","raw_affiliation_strings":["LSV"],"raw_orcid":"https://orcid.org/0000-0001-5879-3304","affiliations":[{"raw_affiliation_string":"LSV","institution_ids":["https://openalex.org/I4210104198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210104198"],"apc_list":null,"apc_paid":null,"fwci":0.2536,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.57752419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"7","first_page":"752","last_page":"832"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9954000115394592,"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":0.9954000115394592,"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":0.9937000274658203,"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/T10639","display_name":"Advanced Software Engineering Methodologies","score":0.9742000102996826,"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/closure","display_name":"Closure (psychology)","score":0.7808716297149658},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6105822324752808},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5895430445671082},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5744175910949707},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5615355968475342},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.530983030796051},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5261955857276917},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5130966901779175},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.46168771386146545},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4482561945915222},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4268408715724945},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3843016028404236},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3749619126319885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3330107629299164},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32432860136032104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12283369898796082},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08655911684036255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07297199964523315},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.05390357971191406}],"concepts":[{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7808716297149658},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6105822324752808},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5895430445671082},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5744175910949707},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5615355968475342},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.530983030796051},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5261955857276917},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5130966901779175},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.46168771386146545},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4482561945915222},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4268408715724945},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3843016028404236},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3749619126319885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3330107629299164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32432860136032104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12283369898796082},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08655911684036255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07297199964523315},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.05390357971191406},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1017/s0960129520000195","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129520000195","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:drops-oai.dagstuhl.de:1844","is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"mag:2949888985","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0902.1587v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:doi:10.4230/lipics.stacs.2009.1844","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"pmh:oai:HAL:hal-03186488v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03186488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science, 2020, 30 (7), pp.752-832. ⟨10.1017/S0960129520000195⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03195833v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-03195833","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Leibniz-Zentrum f\u00fcr Informatik. Proceedings of the 26th Annual Symposium on Theoretical Aspects of Computer Science (STACS'09), volume 3 of Leibniz International Proceedings in Informatics, Freiburg, Germany., pp.433-444, 2009","raw_type":"info:eu-repo/semantics/bookPart"},{"id":"pmh:oai:HAL:inria-00359699v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00359699","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. pp.433-444","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.4230/lipics.stacs.2009.1844","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.stacs.2009.1844","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"mag:2949888985","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0902.1587v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4076119974","display_name":"IDEAL-BASED ALGORITHMS FOR VASSES AND WELL-STRUCTURED SYSTEMS","funder_award_id":"ANR-17-CE40-0028","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W160704552","https://openalex.org/W1525647423","https://openalex.org/W1541630626","https://openalex.org/W1543926679","https://openalex.org/W1574642627","https://openalex.org/W1763122816","https://openalex.org/W1965726041","https://openalex.org/W1965784613","https://openalex.org/W1967174286","https://openalex.org/W1969430156","https://openalex.org/W1984379137","https://openalex.org/W1993941031","https://openalex.org/W2005220910","https://openalex.org/W2008853089","https://openalex.org/W2010265885","https://openalex.org/W2011751050","https://openalex.org/W2035020702","https://openalex.org/W2036564813","https://openalex.org/W2052306562","https://openalex.org/W2053229198","https://openalex.org/W2076508310","https://openalex.org/W2086340783","https://openalex.org/W2087997226","https://openalex.org/W2106001218","https://openalex.org/W2123160677","https://openalex.org/W2132546292","https://openalex.org/W2151637592","https://openalex.org/W2157390113","https://openalex.org/W2160527279","https://openalex.org/W2231192532","https://openalex.org/W2316437449","https://openalex.org/W2331307912","https://openalex.org/W2522551148","https://openalex.org/W2910122182","https://openalex.org/W2914212232","https://openalex.org/W3046469503","https://openalex.org/W4230919050","https://openalex.org/W6634657987","https://openalex.org/W6640003548","https://openalex.org/W6640507295","https://openalex.org/W6653116083","https://openalex.org/W6655199249","https://openalex.org/W6671555141","https://openalex.org/W6678029567","https://openalex.org/W6678257188","https://openalex.org/W6678575093","https://openalex.org/W6682498220","https://openalex.org/W6782104112"],"related_works":["https://openalex.org/W1967174286","https://openalex.org/W2740735804","https://openalex.org/W55688645","https://openalex.org/W2097924536","https://openalex.org/W2094549900","https://openalex.org/W2165634758","https://openalex.org/W2994835914","https://openalex.org/W3131913811","https://openalex.org/W205321414","https://openalex.org/W2755841465","https://openalex.org/W2914322538","https://openalex.org/W2098009311","https://openalex.org/W1777272357","https://openalex.org/W3007353884","https://openalex.org/W2951239978","https://openalex.org/W1616786368","https://openalex.org/W2088537505","https://openalex.org/W2900346622","https://openalex.org/W1969652023","https://openalex.org/W2139544303"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"define":[2,126],"representations":[3,42,59,93],"for":[4,16,90],"downward-closed":[5,110],"subsets":[6,18],"of":[7,11,19,24,32,35,37,48,53,83,94,96,98,102,108,112,129,131,136,159],"a":[8,109,115],"rich":[9],"family":[10,23],"well-quasi-orders,":[12,132],"and":[13,74,78,119,133],"more":[14,51,106,134,153],"generally":[15,52,107,154],"closed":[17,55,161],"an":[20],"even":[21],"richer":[22],"Noetherian":[25,137],"topological":[26],"spaces.":[27,138],"This":[28],"includes":[29],"the":[30,58,65,88,99,145],"cases":[31],"finite":[33,38,46,76,79,92],"words,":[34],"multisets,":[36],"trees,":[39],"notably.":[40],"Those":[41],"are":[43,62],"given":[44],"as":[45],"unions":[47,77],"ideals,":[49],"or":[50,105,152],"irreducible":[54,160],"subsets.":[56,162],"All":[57],"we":[60,68,123,125,142],"explore":[61],"computable,":[63],"in":[64,87,114],"sense":[66],"that":[67,71,144,156],"exhibit":[69],"algorithms":[70],"decide":[72],"inclusion,":[73],"compute":[75],"intersections.":[80],"The":[81],"origin":[82],"this":[84,120],"work":[85],"lies":[86],"need":[89],"computing":[91],"sets":[95],"successors":[97],"downward":[100],"closure":[101],"one":[103],"state,":[104],"set":[111],"states,":[113],"well-structured":[116],"transition":[117],"system,":[118],"is":[121],"where":[122],"start:":[124],"adequate":[127],"notions":[128],"completions":[130,147],"generally,":[135],"For":[139],"verification":[140],"purposes,":[141],"argue":[143],"required":[146],"must":[148],"be":[149],"ideal":[150],"completions,":[151],"sobrifications,":[155],"is,":[157],"spaces":[158]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}