{"id":"https://openalex.org/W4293399521","doi":"https://doi.org/10.1007/978-3-031-15839-1_1","title":"Algebraic Model Checking for\u00a0Discrete Linear Dynamical Systems","display_name":"Algebraic Model Checking for\u00a0Discrete Linear Dynamical Systems","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4293399521","doi":"https://doi.org/10.1007/978-3-031-15839-1_1"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-15839-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-15839-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-15839-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-15839-1_1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007752336","display_name":"Florian Luca","orcid":"https://orcid.org/0000-0003-1321-4422"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Florian Luca","raw_affiliation_strings":["School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045412407","display_name":"Jo\u00ebl Ouaknine","orcid":"https://orcid.org/0000-0003-0031-9356"},"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":"Jo\u00ebl Ouaknine","raw_affiliation_strings":["Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210121786"]}]},{"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"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Worrell","raw_affiliation_strings":["Department of Computer Science, Oxford University, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Oxford University, Oxford, UK","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045412407"],"corresponding_institution_ids":["https://openalex.org/I4210121786"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":2.6524,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.90669326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973000288009644,"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":0.9965000152587891,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6858025193214417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6600396633148193},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.6202582120895386},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.5726175308227539},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5666958689689636},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5578199028968811},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5098440051078796},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5081536769866943},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.48411357402801514},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48291775584220886},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.46538296341896057},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4404314160346985},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.42738550901412964},{"id":"https://openalex.org/keywords/relevance","display_name":"Relevance (law)","score":0.4178297519683838},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.330883651971817},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2502624988555908},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16429686546325684}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6858025193214417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6600396633148193},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.6202582120895386},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.5726175308227539},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5666958689689636},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5578199028968811},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5098440051078796},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5081536769866943},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.48411357402801514},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48291775584220886},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46538296341896057},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4404314160346985},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.42738550901412964},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.4178297519683838},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.330883651971817},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2502624988555908},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16429686546325684},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-031-15839-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-15839-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-15839-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:7b4db5ba-777f-416b-a8fe-40324aec7788","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:7b4db5ba-777f-416b-a8fe-40324aec7788","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Conference item"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-15839-1_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-15839-1_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-15839-1_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7300000190734863,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293399521.pdf","grobid_xml":"https://content.openalex.org/works/W4293399521.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W55887128","https://openalex.org/W177509178","https://openalex.org/W1505135855","https://openalex.org/W1530375435","https://openalex.org/W1549008998","https://openalex.org/W1561261246","https://openalex.org/W1575647584","https://openalex.org/W1592840252","https://openalex.org/W1797219784","https://openalex.org/W1864094877","https://openalex.org/W1983764301","https://openalex.org/W1991004801","https://openalex.org/W1996102424","https://openalex.org/W2021112905","https://openalex.org/W2031633647","https://openalex.org/W2034774429","https://openalex.org/W2038157046","https://openalex.org/W2062077910","https://openalex.org/W2062651539","https://openalex.org/W2121365859","https://openalex.org/W2124909257","https://openalex.org/W2209422068","https://openalex.org/W2243432867","https://openalex.org/W2585298200","https://openalex.org/W2605065382","https://openalex.org/W2953344520","https://openalex.org/W2963416205","https://openalex.org/W2963754540","https://openalex.org/W2963938058","https://openalex.org/W2981410213","https://openalex.org/W3014334551","https://openalex.org/W3116230937","https://openalex.org/W4205178514","https://openalex.org/W4205709417","https://openalex.org/W4210631930","https://openalex.org/W4241950961","https://openalex.org/W4247052524","https://openalex.org/W4248689402","https://openalex.org/W4283452761","https://openalex.org/W4289856130"],"related_works":["https://openalex.org/W2746280673","https://openalex.org/W1541871911","https://openalex.org/W2152996796","https://openalex.org/W1594593035","https://openalex.org/W2050811761","https://openalex.org/W2119813522","https://openalex.org/W2999509083","https://openalex.org/W2230606337","https://openalex.org/W2573078457","https://openalex.org/W2560415449"],"abstract_inverted_index":{"Abstract":[0],"Model":[1],"checking":[2,82],"infinite-state":[3,26],"systems":[4,35],"is":[5,77,98],"one":[6],"of":[7,25,59,75,80,89,106,149],"the":[8,44,54,78,86,123,134,139,146],"central":[9],"challenges":[10],"in":[11,38,43],"automated":[12],"verification.":[13],"In":[14],"this":[15,108],"survey":[16],"we":[17],"focus":[18],"on":[19,85,118,133,144],"an":[20],"important":[21],"and":[22,57,66,94,136,153],"fundamental":[23],"subclass":[24],"systems,":[27,65,68],"namely":[28],"discrete":[29],"linear":[30,91,119,150,154],"dynamical":[31,92,155],"systems.":[32,156],"While":[33],"such":[34],"are":[36],"ubiquitous":[37],"mathematics,":[39],"physics,":[40],"engineering,":[41],"etc.,":[42],"present":[45],"context":[46],"our":[47,95],"motivation":[48],"stems":[49],"from":[50],"their":[51],"relevance":[52],"to":[53,99,113,129,137],"formal":[55],"analysis":[56],"verification":[58],"program":[60],"loops,":[61],"weighted":[62],"automata,":[63],"hybrid":[64],"control":[67],"amongst":[69],"many":[70],"others.":[71],"Our":[72],"main":[73],"object":[74],"study":[76],"problem":[79,109],"model":[81],"temporal":[83],"properties":[84,107],"infinite":[87],"orbit":[88],"a":[90,103],"system,":[93],"principal":[96],"contribution":[97],"show":[100],"that":[101],"for":[102,141],"rich":[104],"class":[105],"can":[110],"be":[111],"reduced":[112],"certain":[114],"classical":[115],"decision":[116],"problems":[117],"recurrence":[120,151],"sequences,":[121],"notably":[122],"Skolem":[124],"Problem.":[125],"This":[126],"leads":[127],"us":[128],"discuss":[130],"recent":[131],"advances":[132],"latter":[135],"highlight":[138],"prospects":[140],"further":[142],"progress":[143],"charting":[145],"algorithmic":[147],"landscape":[148],"sequences":[152]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}