{"id":"https://openalex.org/W7128917963","doi":"https://doi.org/10.1007/s11047-025-10060-7","title":"Encoding reaction systems in Petri nets","display_name":"Encoding reaction systems in Petri nets","publication_year":2026,"publication_date":"2026-02-14","ids":{"openalex":"https://openalex.org/W7128917963","doi":"https://doi.org/10.1007/s11047-025-10060-7"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-025-10060-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10060-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10060-7.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10060-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042490356","display_name":"Maciej Koutny","orcid":"https://orcid.org/0000-0003-4563-1378"},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Maciej Koutny","raw_affiliation_strings":["School of Computing Science, Newcastle University, Newcastle upon Tyne, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing Science, Newcastle University, Newcastle upon Tyne, UK","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036094384","display_name":"\u0141ukasz Mikulski","orcid":"https://orcid.org/0000-0002-6711-557X"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"\u0141ukasz Mikulski","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Toru\u0144, Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Toru\u0144, Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042490356"],"corresponding_institution_ids":["https://openalex.org/I84884186"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23228716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.8956999778747559,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.8956999778747559,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.03240000084042549,"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":0.02070000022649765,"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/petri-net","display_name":"Petri net","score":0.91839998960495},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.5978000164031982},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5605000257492065},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49140000343322754},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4023999869823456},{"id":"https://openalex.org/keywords/natural-computing","display_name":"Natural computing","score":0.3977999985218048},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.39250001311302185},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.3882000148296356},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.37229999899864197}],"concepts":[{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.91839998960495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6940000057220459},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5605000257492065},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5200999975204468},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49140000343322754},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C192979234","wikidata":"https://www.wikidata.org/wiki/Q176890","display_name":"Natural computing","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C152662350","wikidata":"https://www.wikidata.org/wiki/Q815297","display_name":"Systems biology","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C136155141","wikidata":"https://www.wikidata.org/wiki/Q7247260","display_name":"Process architecture","level":3,"score":0.29679998755455017},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C70388272","wikidata":"https://www.wikidata.org/wiki/Q5968558","display_name":"IBM","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C1337776","wikidata":"https://www.wikidata.org/wiki/Q1941955","display_name":"Facilitation","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11047-025-10060-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10060-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10060-7.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11047-025-10060-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10060-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10060-7.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G920233500","display_name":null,"funder_award_id":"RPG-2022-025","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128917963.pdf","grobid_xml":"https://content.openalex.org/works/W7128917963.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W66670465","https://openalex.org/W1491190094","https://openalex.org/W1510349321","https://openalex.org/W1576317809","https://openalex.org/W1972648361","https://openalex.org/W1993742654","https://openalex.org/W1995984957","https://openalex.org/W2132059948","https://openalex.org/W2138447175","https://openalex.org/W2503470518","https://openalex.org/W3166664925","https://openalex.org/W4400725385","https://openalex.org/W4400957545"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Reaction":[1],"systems":[2,52,77,132,158,253],"are":[3,27,38],"rooted":[4],"in":[5,127,195,228,265],"processes":[6,26],"inspired":[7],"by":[8,29,95,133,258],"the":[9,12,19,30,41,81,104,107,175,185,196,212,229,232],"functioning":[10],"of":[11,32,44,60,69,75,83,87,89,97,106,130,135,155,177,188,198,231,278],"living":[13],"cell.":[14],"The":[15,72,261],"key":[16],"idea":[17],"behind":[18],"resulting":[20],"formal":[21],"model":[22,59,74],"is":[23,78,103,172,226,268],"that":[24,171,225],"such":[25,36,141],"determined":[28],"interactions":[31,37],"biochemical":[33],"reactions.":[34,98],"Moreover,":[35],"based":[39,79,173],"on":[40,80,174],"fundamental":[42],"mechanisms":[43],"facilitation":[45],"and":[46,65,91,109,139,209,270],"inhibition.":[47],"Since":[48],"their":[49],"inception,":[50],"reaction":[51,76,131,157,179,234,252,279],"have":[53],"developed":[54],"into":[55,125,191],"an":[56],"extensively":[57],"investigated":[58],"computation":[61],"with":[62,162,217,222,255],"unique":[63],"characteristics":[64],"a":[66,168,178,192,199,203,223,248,273],"wide":[67],"range":[68],"potential":[70],"applications.":[71],"semantical":[73],"concept":[82],"system":[84,180,187],"states":[85],"consisting":[86],"sets":[88,96],"entities,":[90,108],"state":[92],"transformations":[93],"enacted":[94],"Another":[99],"important":[100],"behavioural":[101],"property":[102],"non-permanency":[105],"so":[110],"data":[111],"persistence":[112],"has":[113],"to":[114,122,246],"be":[115,123,244],"consciously":[116],"implemented.":[117],"Issues":[118],"like":[119],"this":[120,146,218,240,266],"need":[121],"taken":[124],"account":[126],"all":[128],"simulations":[129],"means":[134],"other":[136],"existing":[137],"models":[138],"tools,":[140],"as":[142],"Petri":[143,152,193],"nets.":[144],"In":[145,211],"paper,":[147],"we":[148,215],"provide":[149,247,272],"four":[150],"different":[151],"net":[153,194],"encodings":[154],"basic":[156],"operating":[159,254],"without":[160],"interacting":[161],"external":[163],"environment.":[164],"We":[165,236],"start":[166],"from":[167],"naive":[169],"encoding":[170,242,250,262],"behaviour":[176],"$$\\mathscr":[181,189],"{R}$$":[182,190],"only,":[183],"transforming":[184],"transition":[186],"form":[197],"marked":[200],"graph.":[201],"Such":[202],"solution":[204,224],"introduces":[205],"exponentially":[206],"many":[207],"places":[208],"transitions.":[210],"subsequent":[213],"encodings,":[214],"cope":[216],"exponentiality":[219],"ending":[220],"up":[221],"polynomial":[227,241,249],"size":[230],"original":[233],"system.":[235],"then":[237],"show":[238],"how":[239],"can":[243,271],"adapted":[245],"for":[251,275],"contexts":[256],"provided":[257],"context":[259],"automata.":[260],"method":[263],"proposed":[264],"paper":[267],"modular":[269],"basis":[274],"compositional":[276],"construction":[277],"systems.":[280]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-02-15T00:00:00"}