{"id":"https://openalex.org/W2592856594","doi":"https://doi.org/10.1145/3049797.3049798","title":"On the Polytope Escape Problem for Continuous Linear Dynamical Systems","display_name":"On the Polytope Escape Problem for Continuous Linear Dynamical Systems","publication_year":2017,"publication_date":"2017-04-13","ids":{"openalex":"https://openalex.org/W2592856594","doi":"https://doi.org/10.1145/3049797.3049798","mag":"2592856594"},"language":"en","primary_location":{"id":"doi:10.1145/3049797.3049798","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3049797.3049798","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.03166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Joel 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":true,"raw_author_name":"Joel Ouaknine","raw_affiliation_strings":["MPI-SWS and Oxford University, Saarbruecken, Germany"],"affiliations":[{"raw_affiliation_string":"MPI-SWS and Oxford University, Saarbruecken, Germany","institution_ids":["https://openalex.org/I4210121786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Joao Sousa-Pinto","orcid":null},"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":"Joao Sousa-Pinto","raw_affiliation_strings":["Oxford University, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Oxford University, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":null,"display_name":"James Worrell","orcid":null},"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":["Oxford University, Oxford, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Oxford University, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210121786"],"apc_list":null,"apc_paid":null,"fwci":0.474,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64537153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"11","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9969000220298767,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9969000220298767,"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/T10142","display_name":"Formal Methods in Verification","score":0.9937999844551086,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.987500011920929,"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/polytope","display_name":"Polytope","score":0.7268999814987183},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.5526999831199646},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5354999899864197},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.49959999322891235},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4909000098705292},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.487199991941452},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4618000090122223},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.45170000195503235},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4142000079154968},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.39239999651908875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7649999856948853},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7268999814987183},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5354999899864197},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.49959999322891235},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.487199991941452},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.45170000195503235},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4142000079154968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40849998593330383},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38269999623298645},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.3677000105381012},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.34529998898506165},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.33070001006126404},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30230000615119934},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.2809000015258789},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.27070000767707825},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.26980000734329224},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3049797.3049798","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3049797.3049798","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1507.03166","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.03166","pdf_url":"https://arxiv.org/pdf/1507.03166","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.03166","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.03166","pdf_url":"https://arxiv.org/pdf/1507.03166","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2044065458","display_name":null,"funder_award_id":"321171,648701","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"}],"funders":[{"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1561261246","https://openalex.org/W1575739325","https://openalex.org/W1760322535","https://openalex.org/W1987631685","https://openalex.org/W1988289336","https://openalex.org/W2024997126","https://openalex.org/W2048600779","https://openalex.org/W2067754486","https://openalex.org/W2113789941","https://openalex.org/W2128031447","https://openalex.org/W2141040012","https://openalex.org/W2155969572","https://openalex.org/W2370502869","https://openalex.org/W2386123026","https://openalex.org/W4255769949","https://openalex.org/W4298290503","https://openalex.org/W6652809280","https://openalex.org/W6669754204","https://openalex.org/W7005335020"],"related_works":[],"abstract_inverted_index":{"The":[0,80],"Polytope":[1],"Escape":[2],"Problem":[3],"for":[4,90],"continuous":[5],"linear":[6,74],"dynamical":[7],"systems":[8],"consists":[9],"of":[10,42,73,86,94,111],"deciding,":[11],"given":[12],"an":[13,32],"affine":[14],"function":[15],"f:Rd":[16],"->":[17],"Rd":[18],"and":[19,105,114],"a":[20,83],"convex":[21],"polytope":[22],"P\u2286":[23],"Rd,":[24],"both":[25],"with":[26,76],"rational":[27],"descriptions,":[28],"whether":[29],"there":[30],"exists":[31],"initial":[33],"point":[34],"x0":[35,53],"in":[36,57,66],"P":[37],"such":[38],"that":[39,61],"the":[40,43,47,70,87,91],"trajectory":[41],"unique":[44],"solution":[45],"to":[46,69,101],"differential":[48],"equation:":[49],"\u00b7x(t)=f(x(t))":[50],"x":[51],"0=":[52],"is":[54,64,82,99],"entirely":[55],"contained":[56],"P.":[58],"We":[59],"show":[60],"this":[62],"problem":[63,89],"reducible":[65],"polynomial":[67],"time":[68],"decision":[71,88],"version":[72],"programming":[75],"real":[77,95],"algebraic":[78],"coefficients.":[79],"latter":[81],"special":[84],"case":[85],"existential":[92],"theory":[93],"closed":[96],"fields,":[97],"which":[98],"known":[100],"lie":[102],"between":[103],"NP":[104],"PSPACE.":[106],"Our":[107],"algorithm":[108],"makes":[109],"use":[110],"spectral":[112],"techniques":[113],"relies,":[115],"among":[116],"others,":[117],"on":[118],"tools":[119],"from":[120],"Diophantine":[121],"approximation.":[122]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2017-03-16T00:00:00"}