{"id":"https://openalex.org/W2344793144","doi":"https://doi.org/10.1109/tsmc.2015.2507162","title":"Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices","display_name":"Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices","publication_year":2015,"publication_date":"2015-12-24","ids":{"openalex":"https://openalex.org/W2344793144","doi":"https://doi.org/10.1109/tsmc.2015.2507162","mag":"2344793144"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2015.2507162","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2015.2507162","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081098250","display_name":"Xiaoguang Han","orcid":"https://orcid.org/0000-0003-0810-259X"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoguang Han","raw_affiliation_strings":["Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073105796","display_name":"Zengqiang Chen","orcid":"https://orcid.org/0000-0002-1415-4073"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]},{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengqiang Chen","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin, China","College of Science, Civil Aviation University of China, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin, China","institution_ids":["https://openalex.org/I28813325"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019147450","display_name":"Zhongxin Liu","orcid":"https://orcid.org/0000-0002-3565-4800"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongxin Liu","raw_affiliation_strings":["College of Computer and Control Engineering, Nankai University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615838","display_name":"Qing Zhang","orcid":"https://orcid.org/0000-0003-3941-4764"},"institutions":[{"id":"https://openalex.org/I28813325","display_name":"Civil Aviation University of China","ror":"https://ror.org/03je71k37","country_code":"CN","type":"education","lineage":["https://openalex.org/I28813325"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qing Zhang","raw_affiliation_strings":["College of Science, Civil Aviation University of China, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Civil Aviation University of China, Tianjin, China","institution_ids":["https://openalex.org/I28813325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.8124,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.98580848,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"47","issue":"3","first_page":"531","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","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/T11125","display_name":"Petri Nets in System Modeling","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/T10142","display_name":"Formal Methods in Verification","score":0.9939000010490417,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/siphon","display_name":"Siphon (mollusc)","score":0.7682796716690063},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6978604793548584},{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.6632471084594727},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6127960681915283},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4912504553794861},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4804777204990387},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.459328830242157},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4542343020439148},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4340587854385376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34594571590423584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1362144947052002},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12624087929725647}],"concepts":[{"id":"https://openalex.org/C163629137","wikidata":"https://www.wikidata.org/wiki/Q1276903","display_name":"Siphon (mollusc)","level":2,"score":0.7682796716690063},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6978604793548584},{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.6632471084594727},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6127960681915283},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4912504553794861},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4804777204990387},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.459328830242157},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4542343020439148},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4340587854385376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34594571590423584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1362144947052002},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12624087929725647},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2015.2507162","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2015.2507162","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1374639957","display_name":null,"funder_award_id":"61573200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1635134894","display_name":null,"funder_award_id":"61573199","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4285890512","display_name":null,"funder_award_id":"14JCYBJC18700","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"},{"id":"https://openalex.org/G597355347","display_name":null,"funder_award_id":"13JCYBJC17400","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323993","display_name":"Natural Science Foundation of Tianjin City","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W141673210","https://openalex.org/W400067794","https://openalex.org/W567151721","https://openalex.org/W940409914","https://openalex.org/W1519324376","https://openalex.org/W1546320162","https://openalex.org/W1587663028","https://openalex.org/W1980149643","https://openalex.org/W1991720013","https://openalex.org/W1994188141","https://openalex.org/W1996109622","https://openalex.org/W1997821888","https://openalex.org/W2073458555","https://openalex.org/W2089545832","https://openalex.org/W2090408760","https://openalex.org/W2093489050","https://openalex.org/W2095603938","https://openalex.org/W2117011945","https://openalex.org/W2122471000","https://openalex.org/W2127349283","https://openalex.org/W2140872435","https://openalex.org/W2144525166","https://openalex.org/W2146738006","https://openalex.org/W2148357359","https://openalex.org/W2161788716","https://openalex.org/W2311033460","https://openalex.org/W2397401118","https://openalex.org/W2509841691","https://openalex.org/W6605773425","https://openalex.org/W6632797247","https://openalex.org/W6712712927"],"related_works":["https://openalex.org/W1997821888","https://openalex.org/W2090242624","https://openalex.org/W2122471000","https://openalex.org/W2043721415","https://openalex.org/W2129170313","https://openalex.org/W2310793150","https://openalex.org/W2355845685","https://openalex.org/W2036031969","https://openalex.org/W1995367634","https://openalex.org/W2509039953"],"abstract_inverted_index":{"In":[0],"this":[1,114],"paper,":[2,115],"we":[3],"address":[4],"the":[5,21,32,59,65,106,110],"problems":[6],"of":[7,25,79,109],"enumerating":[8],"siphons":[9,12,49,78,97],"and":[10,62],"minimal":[11,96],"in":[13,50,75,113],"ordinary":[14,51,100],"Petri":[15],"nets":[16],"(PNs)":[17],"by":[18,38],"resorting":[19],"to":[20,46,57,93],"semi-tensor":[22],"product":[23],"(STP)":[24],"matrices.":[26],"First,":[27],"a":[28],"matrix":[29],"equation,":[30],"called":[31],"siphon":[33],"equation":[34],"(SE),":[35],"is":[36,44,55,68,86],"established":[37],"using":[39],"STP.":[40],"Second,":[41],"an":[42,82],"algorithm":[43,85],"proposed":[45,66,111],"calculate":[47],"all":[48,77,95],"PNs.":[52,80,101],"An":[53],"example":[54],"presented":[56],"illustrate":[58],"theoretical":[60],"results":[61,104],"show":[63],"that":[64],"method":[67],"more":[69],"effective":[70],"than":[71],"other":[72],"existing":[73],"methods":[74],"calculating":[76],"Third,":[81],"efficient":[83],"recursion":[84],"also":[87],"proposed,":[88],"which":[89],"can":[90],"be":[91],"applied":[92],"computing":[94],"for":[98],"any":[99],"Last,":[102],"some":[103],"on":[105],"computational":[107],"complexity":[108],"algorithms,":[112],"are":[116],"provided,":[117],"as":[118,120],"well":[119],"experimental":[121],"results.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
