{"id":"https://openalex.org/W2089663991","doi":"https://doi.org/10.1017/s0960129506005664","title":"Transition systems, link graphs and Petri nets","display_name":"Transition systems, link graphs and Petri nets","publication_year":2006,"publication_date":"2006-12-01","ids":{"openalex":"https://openalex.org/W2089663991","doi":"https://doi.org/10.1017/s0960129506005664","mag":"2089663991"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129506005664","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005664","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/83cb117a-a603-477b-b0b5-5eb7e8fdd145","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065954613","display_name":"James J. Leifer","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"JAMES J. LEIFER","raw_affiliation_strings":["INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France Email:","INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France Email: James.Leifer@inria.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France Email:","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France Email: James.Leifer@inria.fr#TAB#","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114258078","display_name":"Robin Milner","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"ROBIN MILNER","raw_affiliation_strings":["University of Cambridge, Computer Laboratory, JJ Thomson Avenue, Cambridge CB3 0FD, U.K"],"affiliations":[{"raw_affiliation_string":"University of Cambridge, Computer Laboratory, JJ Thomson Avenue, Cambridge CB3 0FD, U.K","institution_ids":["https://openalex.org/I4210096386","https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065954613"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":5.73,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.96489987,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"06","first_page":"989","last_page":"989"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10679","display_name":"Service-Oriented Architecture and Web Services","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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":0.8833778500556946},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6773892045021057},{"id":"https://openalex.org/keywords/link","display_name":"Link (geometry)","score":0.6705614924430847},{"id":"https://openalex.org/keywords/transition-system","display_name":"Transition system","score":0.6346839666366577},{"id":"https://openalex.org/keywords/preorder","display_name":"Preorder","score":0.6313295364379883},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5663696527481079},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5448018908500671},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.5400872826576233},{"id":"https://openalex.org/keywords/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.43981385231018066},{"id":"https://openalex.org/keywords/concurrency","display_name":"Concurrency","score":0.4379737377166748},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3910940885543823},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36135199666023254},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32414180040359497},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1691407561302185},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.15232965350151062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10796251893043518}],"concepts":[{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.8833778500556946},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6773892045021057},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.6705614924430847},{"id":"https://openalex.org/C2779167558","wikidata":"https://www.wikidata.org/wiki/Q176468","display_name":"Transition system","level":2,"score":0.6346839666366577},{"id":"https://openalex.org/C2333172","wikidata":"https://www.wikidata.org/wiki/Q1425985","display_name":"Preorder","level":2,"score":0.6313295364379883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5663696527481079},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5448018908500671},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.5400872826576233},{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.43981385231018066},{"id":"https://openalex.org/C193702766","wikidata":"https://www.wikidata.org/wiki/Q1414548","display_name":"Concurrency","level":2,"score":0.4379737377166748},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3910940885543823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36135199666023254},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32414180040359497},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1691407561302185},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.15232965350151062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10796251893043518},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0960129506005664","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005664","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/83cb117a-a603-477b-b0b5-5eb7e8fdd145","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/83cb117a-a603-477b-b0b5-5eb7e8fdd145","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Leifer, J J & Milner, R 2006, 'Transition systems, link graphs and Petri nets', Mathematical Structures in Computer Science, vol. 16, no. 6, pp. 989-1047. https://doi.org/10.1017/S0960129506005664","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.1344","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-598.pdf","raw_type":"text"},{"id":"pmh:oai:pure.ed.ac.uk:publications/83cb117a-a603-477b-b0b5-5eb7e8fdd145","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11820/83cb117a-a603-477b-b0b5-5eb7e8fdd145","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/83cb117a-a603-477b-b0b5-5eb7e8fdd145","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/83cb117a-a603-477b-b0b5-5eb7e8fdd145","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Leifer, J J & Milner, R 2006, 'Transition systems, link graphs and Petri nets', Mathematical Structures in Computer Science, vol. 16, no. 6, pp. 989-1047. https://doi.org/10.1017/S0960129506005664","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W159994793","https://openalex.org/W203609956","https://openalex.org/W1484116835","https://openalex.org/W1490559739","https://openalex.org/W1495106476","https://openalex.org/W1495299640","https://openalex.org/W1500576982","https://openalex.org/W1524658540","https://openalex.org/W1528214111","https://openalex.org/W1539392311","https://openalex.org/W1547562281","https://openalex.org/W1548324490","https://openalex.org/W1555729963","https://openalex.org/W1556091851","https://openalex.org/W1559264271","https://openalex.org/W1574796876","https://openalex.org/W1587000168","https://openalex.org/W1591694044","https://openalex.org/W1591745554","https://openalex.org/W1605829531","https://openalex.org/W1836115201","https://openalex.org/W1841342726","https://openalex.org/W1846189533","https://openalex.org/W1895954544","https://openalex.org/W1909063750","https://openalex.org/W1932110987","https://openalex.org/W1971095420","https://openalex.org/W1984689429","https://openalex.org/W1999706742","https://openalex.org/W2007006124","https://openalex.org/W2013672985","https://openalex.org/W2049924207","https://openalex.org/W2050942832","https://openalex.org/W2055378322","https://openalex.org/W2057814731","https://openalex.org/W2075050099","https://openalex.org/W2076632469","https://openalex.org/W2078060182","https://openalex.org/W2083127081","https://openalex.org/W2088941870","https://openalex.org/W2095421079","https://openalex.org/W2102097307","https://openalex.org/W2107674601","https://openalex.org/W2110796675","https://openalex.org/W2111587608","https://openalex.org/W2112097795","https://openalex.org/W2112736696","https://openalex.org/W2118686544","https://openalex.org/W2120076632","https://openalex.org/W2128932399","https://openalex.org/W2132981613","https://openalex.org/W2137865376","https://openalex.org/W2158942489","https://openalex.org/W2169849200","https://openalex.org/W2176300081","https://openalex.org/W2284263109","https://openalex.org/W2294530123","https://openalex.org/W2295014926","https://openalex.org/W2912003593","https://openalex.org/W3029749730","https://openalex.org/W3144368627","https://openalex.org/W3144771442","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1543378523","https://openalex.org/W2916743419","https://openalex.org/W2381491984","https://openalex.org/W1529681579","https://openalex.org/W2257573499","https://openalex.org/W1847176793","https://openalex.org/W1980200158","https://openalex.org/W2091203523","https://openalex.org/W1513546254","https://openalex.org/W2125164140"],"abstract_inverted_index":{"A":[0],"framework":[1,13,85],"is":[2,14,86,113,116,132],"defined":[3],"within":[4,25],"which":[5,18,26,63,78,97],"reactive":[6,27,173],"systems":[7,28,40,174],"can":[8,29,41],"be":[9,30,42,67],"studied":[10],"formally.":[11],"The":[12,69,107,148],"based":[15],"on":[16,72],"s-categories,":[17],"are":[19,64],"a":[20,35,89,99,128,139,152,166],"new":[21],"variety":[22,100],"of":[23,75,101,110,142,168,172],"categories":[24],"set":[31],"up":[32],"in":[33,47,145],"such":[34,54],"way":[36],"that":[37],"labelled":[38,129],"transition":[39,130,149],"uniformly":[43],"extracted.":[44],"These":[45],"lead":[46],"turn":[48],"to":[49,66,88,119,138],"behavioural":[50],"preorders":[51],"and":[52,61,175],"equivalences,":[53],"as":[55,94],"the":[56,73,83,161,169],"failures":[57],"preorder":[58],"(treated":[59],"elsewhere)":[60],"bisimilarity,":[62],"guaranteed":[65],"congruential.":[68],"theory":[70,109,171],"rests":[71],"notion":[74,141],"relative":[76],"pushout,":[77],"was":[79],"previously":[80],"introduced":[81],"by":[82],"authors.The":[84],"applied":[87,118],"particular":[90],"graphical":[91],"model,":[92],"known":[93,179],"link":[95,111,176],"graphs,":[96],"encompasses":[98],"calculi":[102],"for":[103,134],"mobile":[104],"distributed":[105],"processes.":[106],"specific":[108,180],"graphs":[112,177],"developed.":[114],"It":[115],"then":[117],"an":[120],"established":[121],"calculus,":[122],"namely":[123],"condition-event":[124,135],"Petri":[125],"nets.In":[126],"particular,":[127],"system":[131,150],"derived":[133,158],"nets,":[136],"corresponding":[137],"natural":[140],"observable":[143,162],"actions":[144],"Petri-net":[146],"theory.":[147],"yields":[151,165],"congruential":[153],"bisimilarity":[154],"coinciding":[155],"with":[156],"one":[157],"directly":[159],"from":[160],"actions.":[163],"This":[164],"calibration":[167],"general":[170],"against":[178],"theories.":[181]},"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}