{"id":"https://openalex.org/W2946260851","doi":"https://doi.org/10.1145/3286487","title":"On the Decidability of Membership in Matrix-exponential Semigroups","display_name":"On the Decidability of Membership in Matrix-exponential Semigroups","publication_year":2019,"publication_date":"2019-05-23","ids":{"openalex":"https://openalex.org/W2946260851","doi":"https://doi.org/10.1145/3286487","mag":"2946260851"},"language":"en","primary_location":{"id":"doi:10.1145/3286487","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3286487","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3286487","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3286487","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108955693","display_name":"Jo\u00ebl Ouaknine","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jo\u00ebl Ouaknine","raw_affiliation_strings":["Max Planck Institute for Software Systems, Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2469-2809","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Software Systems, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210121786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072806743","display_name":"Amaury Pouly","orcid":"https://orcid.org/0000-0002-2549-951X"},"institutions":[{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Amaury Pouly","raw_affiliation_strings":["Max Planck Institute for Software Systems, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Software Systems, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210121786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029470639","display_name":"Jo\u00e3o Sousa-Pinto","orcid":"https://orcid.org/0000-0003-2469-2809"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o Sousa-Pinto","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068165188","display_name":"James Worrell","orcid":"https://orcid.org/0000-0001-8151-2443"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Worrell","raw_affiliation_strings":["University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1928,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.51903593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"66","issue":"3","first_page":"1","last_page":"24"},"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/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.8375165462493896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7884413003921509},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.711117148399353},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6333422660827637},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.6173254251480103},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5689133405685425},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5190870761871338},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46882766485214233},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.45854806900024414},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.42876121401786804},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42236292362213135},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32793140411376953},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2762744426727295},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07960847020149231}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8375165462493896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7884413003921509},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.711117148399353},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6333422660827637},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.6173254251480103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5689133405685425},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5190870761871338},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46882766485214233},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.45854806900024414},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.42876121401786804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42236292362213135},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32793140411376953},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2762744426727295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07960847020149231},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3286487","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3286487","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3286487","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03011135v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03011135","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":"Journal of the ACM (JACM), 2019, 66 (3), pp.1-24. ⟨10.1145/3286487⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:21174833-b044-4dde-80ce-d742c1944d81","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:21174833-b044-4dde-80ce-d742c1944d81","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference item"},{"id":"pmh:oai:pure.mpg.de:item_3212855","is_oa":false,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0005-D505-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1145/3286487","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3286487","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3286487","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5699999928474426}],"awards":[{"id":"https://openalex.org/G1659557484","display_name":"Analysis, Verification, and Synthesis for Infinite-State Systems","funder_award_id":"648701","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G2704700155","display_name":null,"funder_award_id":"EP/N008197/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3032849772","display_name":null,"funder_award_id":"TRR 248","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7439426443","display_name":"Verification of Linear Dynamical Systems","funder_award_id":"EP/N008197/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G890954746","display_name":"TRR 248: Grundlagen verst\u00e4ndlicher SoftwareSysteme  f\u00fcr eine nachvollziehbare cyberphysische Welt","funder_award_id":"389792660","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2946260851.pdf","grobid_xml":"https://content.openalex.org/works/W2946260851.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W69640471","https://openalex.org/W1496801598","https://openalex.org/W1575739325","https://openalex.org/W1585899462","https://openalex.org/W1592891131","https://openalex.org/W1605256314","https://openalex.org/W1802268423","https://openalex.org/W1966167381","https://openalex.org/W1972422534","https://openalex.org/W1987631685","https://openalex.org/W1989605444","https://openalex.org/W1998501436","https://openalex.org/W2010180140","https://openalex.org/W2016430133","https://openalex.org/W2020140696","https://openalex.org/W2034774429","https://openalex.org/W2047105695","https://openalex.org/W2147340401","https://openalex.org/W2163590987","https://openalex.org/W2187041056","https://openalex.org/W2320126437","https://openalex.org/W2963431677","https://openalex.org/W2991196351","https://openalex.org/W4243055393","https://openalex.org/W4280582130"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W1501430220","https://openalex.org/W2989332944","https://openalex.org/W2021891065","https://openalex.org/W2583549044","https://openalex.org/W2119045600","https://openalex.org/W2584984136","https://openalex.org/W2962928105","https://openalex.org/W2170336571","https://openalex.org/W2020140696"],"abstract_inverted_index":{"We":[0,148],"consider":[1],"the":[2,5,30,44,48,110,154],"decidability":[3,133],"of":[4,29,78,87,98,141,164],"membership":[6,112],"problem":[7,70,86,113],"for":[8,153],"matrix-exponential":[9],"semigroups:":[10],"Given":[11],"k":[12,24,63,130],"\u2208":[13,59],"N":[14],"and":[15,33,65,82,92,102],"square":[16],"matrices":[17],"A":[18,23,53,124,129],"1":[19,125],",":[20,22,25,27,62,126,128],"\u2026":[21,127],"C":[26,40],"all":[28],"same":[31],"dimension":[32],"with":[34],"real":[35],"algebraic":[36,165],"entries,":[37],"decide":[38],"whether":[39],"is":[41,114,135,173],"contained":[42],"in":[43,116,162],"semigroup":[45,111],"generated":[46],"by":[47,136,175],"matrix":[49,90],"exponentials":[50],"exp":[51],"(":[52],"i":[54,58],"t":[55,66],"),":[56],"where":[57],"{":[60],"1,\u2026":[61],"}":[64],"\u2265":[67],"0.":[68],"This":[69],"can":[71],"be":[72],"seen":[73],"as":[74],"a":[75,139,150],"continuous":[76],"analog":[77],"Babai":[79],"et":[80,84],"al.\u2019s":[81,85],"Cai":[83],"solving":[88],"multiplicative":[89],"equations":[91],"has":[93,145],"applications":[94],"to":[95,138],"reachability":[96],"analysis":[97],"linear":[99,160],"hybrid":[100],"automata":[101],"switching":[103],"systems.":[104],"Our":[105],"main":[106],"results":[107],"are":[108],"that":[109,123,144],"undecidable":[115],"general,":[117],"but":[118],"decidable":[119],"if":[120],"we":[121],"assume":[122],"commute.":[131],"The":[132,170],"proof":[134],"reduction":[137,176],"version":[140],"integer":[142],"programming":[143],"transcendental":[146],"constants.":[147],"give":[149],"decision":[151],"procedure":[152],"latter":[155],"using":[156],"Baker\u2019s":[157],"theorem":[158],"on":[159],"forms":[161],"logarithms":[163],"numbers,":[166],"among":[167],"other":[168],"tools.":[169],"undecidability":[171],"result":[172],"shown":[174],"from":[177],"Hilbert\u2019s":[178],"Tenth":[179],"Problem.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}