{"id":"https://openalex.org/W2954429781","doi":"https://doi.org/10.1007/978-3-030-45231-5_32","title":"The Polynomial Complexity of Vector Addition Systems with States","display_name":"The Polynomial Complexity of Vector Addition Systems with States","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2954429781","doi":"https://doi.org/10.1007/978-3-030-45231-5_32","mag":"2954429781"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-45231-5_32","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-45231-5_32","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-45231-5_32.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":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-45231-5_32.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063337176","display_name":"Florian Zuleger","orcid":"https://orcid.org/0000-0003-1468-8398"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Florian Zuleger","raw_affiliation_strings":["TU Wien, \nVienna, Austria","Vienna University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Wien, \nVienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Vienna University of Technology","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063337176"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.3371,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39013934,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"622","last_page":"641"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T11567","display_name":"semigroups and automata theory","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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8073732852935791},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6800597310066223},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6670303344726562},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6002439260482788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.554065465927124},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5360961556434631},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.475645512342453},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.45773956179618835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3914473056793213},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32767587900161743},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22584936022758484},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22344157099723816},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13959285616874695}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8073732852935791},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6800597310066223},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6670303344726562},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6002439260482788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.554065465927124},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5360961556434631},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.475645512342453},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.45773956179618835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3914473056793213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32767587900161743},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22584936022758484},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22344157099723816},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13959285616874695},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/978-3-030-45231-5_32","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-45231-5_32","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-45231-5_32.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:arXiv.org:1907.01076","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.01076","pdf_url":"https://arxiv.org/pdf/1907.01076","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},{"id":"mag:2954429781","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.01076v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:oai:europepmc.org:6700095","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC7788602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7788602","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7788602","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Foundations of Software Science and Computation Structures","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1907.01076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.01076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-45231-5_32","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-45231-5_32","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-45231-5_32.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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2954429781.pdf","grobid_xml":"https://content.openalex.org/works/W2954429781.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W111201530","https://openalex.org/W149631060","https://openalex.org/W188018220","https://openalex.org/W1545777893","https://openalex.org/W1636902686","https://openalex.org/W1863102867","https://openalex.org/W1974179433","https://openalex.org/W2017315323","https://openalex.org/W2028113097","https://openalex.org/W2036526834","https://openalex.org/W2055081868","https://openalex.org/W2078846861","https://openalex.org/W2106001218","https://openalex.org/W2115049824","https://openalex.org/W2206615804","https://openalex.org/W2296248291","https://openalex.org/W2316437449","https://openalex.org/W2394903686","https://openalex.org/W2414818575","https://openalex.org/W2577171054","https://openalex.org/W2962849754","https://openalex.org/W2965991421"],"related_works":["https://openalex.org/W3022740807","https://openalex.org/W1561749771","https://openalex.org/W2003358226","https://openalex.org/W1778948012","https://openalex.org/W2159041477","https://openalex.org/W2947219923","https://openalex.org/W2966363981","https://openalex.org/W2944909810","https://openalex.org/W2135958048","https://openalex.org/W2132032691","https://openalex.org/W2883287107","https://openalex.org/W2962707756","https://openalex.org/W1991092165","https://openalex.org/W1483514891","https://openalex.org/W2291181759","https://openalex.org/W2970483056","https://openalex.org/W2056443473","https://openalex.org/W3179792452","https://openalex.org/W2786829989","https://openalex.org/W2810015330"],"abstract_inverted_index":{"Abstract":[0],"Vector":[1],"addition":[2,27,65,87,134,157],"systems":[3,28],"are":[4,40],"an":[5],"important":[6],"model":[7],"in":[8,16,42,124,127],"theoretical":[9],"computer":[10],"science":[11],"and":[12],"have":[13],"been":[14],"used":[15],"a":[17,32,62,84],"variety":[18],"of":[19,46,57,73,83,108,130,153],"areas.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24,39,51,137],"consider":[25],"vector":[26,64,86,133,156],"with":[29,67,89],"states":[30,68,90],"over":[31],"parameterized":[33],"initial":[34,75,110],"configuration.":[35,76],"For":[36],"these":[37],"systems,":[38],"interested":[41],"the":[43,55,58,71,74,80,106,109,128,131,151,154],"standard":[44],"notion":[45],"computational":[47],"time":[48,126],"complexity,":[49],"i.e.,":[50],"want":[52],"to":[53],"understand":[54],"length":[56],"longest":[59],"trace":[60],"for":[61,97],"fixed":[63],"system":[66,88],"depending":[69],"on":[70],"size":[72,107,129],"We":[77,116],"show":[78,118,138],"that":[79,119,139],"asymptotic":[81],"complexity":[82],"given":[85],"is":[91,105,150],"either":[92],"$$\\varTheta":[93],"(N^k)$$":[94],"<mml:math":[95,145],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u0398</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mi>k</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math>":[96],"some":[98],"computable":[99],"integer":[100],"k":[101,120,142],",":[102,147],"where":[103,148],"N":[104],"configuration,":[111],"or":[112],"at":[113],"least":[114],"exponential.":[115],"further":[117],"can":[121],"be":[122],"computed":[123],"polynomial":[125],"considered":[132,155],"system.":[135,158],"Finally,":[136],"$$1":[140],"\\le":[141,143],"2^n$$":[144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mn>1</mml:mn><mml:mo>\u2264</mml:mo><mml:mi>k</mml:mi><mml:mo>\u2264</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>":[146],"n":[149],"dimension":[152]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}