{"id":"https://openalex.org/W3174611822","doi":"https://doi.org/10.1007/s00236-021-00404-y","title":"Proportional lumpability and proportional bisimilarity","display_name":"Proportional lumpability and proportional bisimilarity","publication_year":2021,"publication_date":"2021-06-21","ids":{"openalex":"https://openalex.org/W3174611822","doi":"https://doi.org/10.1007/s00236-021-00404-y","mag":"3174611822"},"language":"en","primary_location":{"id":"doi:10.1007/s00236-021-00404-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00236-021-00404-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00236-021-00404-y.pdf","source":{"id":"https://openalex.org/S84409463","display_name":"Acta Informatica","issn_l":"0001-5903","issn":["0001-5903","1432-0525"],"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":"Acta Informatica","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/s00236-021-00404-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005581769","display_name":"Andrea Marin","orcid":"https://orcid.org/0000-0002-5958-1204"},"institutions":[{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Marin","raw_affiliation_strings":["Universit\u00e0 Ca\u2019 Foscari Venezia, Venezia, Italy","Universit\u00e0 Ca' Foscari Venezia, Venezia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 Ca\u2019 Foscari Venezia, Venezia, Italy","institution_ids":["https://openalex.org/I149461666"]},{"raw_affiliation_string":"Universit\u00e0 Ca' Foscari Venezia, Venezia, Italy","institution_ids":["https://openalex.org/I149461666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027009916","display_name":"Carla Piazza","orcid":"https://orcid.org/0000-0002-2072-1628"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carla Piazza","raw_affiliation_strings":["Universit\u00e0 di Udine, Udine, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015760641","display_name":"Sabina Rossi","orcid":"https://orcid.org/0000-0002-1189-4439"},"institutions":[{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sabina Rossi","raw_affiliation_strings":["Universit\u00e0 Ca\u2019 Foscari Venezia, Venezia, Italy","Universit\u00e0 Ca' Foscari Venezia, Venezia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-1189-4439","affiliations":[{"raw_affiliation_string":"Universit\u00e0 Ca\u2019 Foscari Venezia, Venezia, Italy","institution_ids":["https://openalex.org/I149461666"]},{"raw_affiliation_string":"Universit\u00e0 Ca' Foscari Venezia, Venezia, Italy","institution_ids":["https://openalex.org/I149461666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7611,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75630987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"2-3","first_page":"211","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9976000189781189,"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":0.9976000189781189,"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":0.9930999875068665,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/markov-chain","display_name":"Markov chain","score":0.7741824984550476},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6925753355026245},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.564408004283905},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5319664478302002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4787851572036743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4737575650215149},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4729875326156616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.424378901720047},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4164566099643707},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.266892671585083},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0970287024974823}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7741824984550476},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6925753355026245},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.564408004283905},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5319664478302002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4787851572036743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4737575650215149},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4729875326156616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.424378901720047},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4164566099643707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.266892671585083},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0970287024974823}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00236-021-00404-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00236-021-00404-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00236-021-00404-y.pdf","source":{"id":"https://openalex.org/S84409463","display_name":"Acta Informatica","issn_l":"0001-5903","issn":["0001-5903","1432-0525"],"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":"Acta Informatica","raw_type":"journal-article"},{"id":"pmh:oai:air.uniud.it:11390/1208602","is_oa":true,"landing_page_url":"http://hdl.handle.net/11390/1208602","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"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":"","raw_type":"262"},{"id":"pmh:oai:iris.unive.it:10278/3744337","is_oa":true,"landing_page_url":"http://hdl.handle.net/10278/3744337","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00236-021-00404-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00236-021-00404-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00236-021-00404-y.pdf","source":{"id":"https://openalex.org/S84409463","display_name":"Acta Informatica","issn_l":"0001-5903","issn":["0001-5903","1432-0525"],"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":"Acta Informatica","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6800000071525574}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320324979","display_name":"Universit\u00e0 degli Studi di Udine","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3174611822.pdf","grobid_xml":"https://content.openalex.org/works/W3174611822.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W43528323","https://openalex.org/W1546525608","https://openalex.org/W1597655219","https://openalex.org/W1830035551","https://openalex.org/W1964665516","https://openalex.org/W1965790781","https://openalex.org/W1979732947","https://openalex.org/W1992534487","https://openalex.org/W1999972524","https://openalex.org/W2021089599","https://openalex.org/W2023563854","https://openalex.org/W2032806006","https://openalex.org/W2044811734","https://openalex.org/W2045291361","https://openalex.org/W2048328443","https://openalex.org/W2065351087","https://openalex.org/W2074012765","https://openalex.org/W2074041201","https://openalex.org/W2075379212","https://openalex.org/W2082381752","https://openalex.org/W2096249059","https://openalex.org/W2101645257","https://openalex.org/W2114710208","https://openalex.org/W2115555017","https://openalex.org/W2124215579","https://openalex.org/W2125739093","https://openalex.org/W2140494267","https://openalex.org/W2161584651","https://openalex.org/W2166528301","https://openalex.org/W2167419136","https://openalex.org/W2295906390","https://openalex.org/W2329912647","https://openalex.org/W2491539874","https://openalex.org/W2804498827","https://openalex.org/W2922196358","https://openalex.org/W3142156004","https://openalex.org/W4206542816","https://openalex.org/W4243653701","https://openalex.org/W4254158247"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W2762130752","https://openalex.org/W2379651310","https://openalex.org/W1541249122","https://openalex.org/W2113019827","https://openalex.org/W2413828414","https://openalex.org/W1487400845","https://openalex.org/W2734407528","https://openalex.org/W2367222340","https://openalex.org/W1841898224"],"abstract_inverted_index":{"Abstract":[0],"In":[1,107],"this":[2,108],"paper,":[3],"we":[4,123,192],"deal":[5],"with":[6,12],"the":[7,13,20,23,57,61,66,78,92,100,116,136,144,159,165,171,174,186,199],"lumpability":[8,32,132,140,184],"approach":[9],"to":[10,19,43,54,152],"cope":[11],"state":[14,38],"space":[15],"explosion":[16],"problem":[17],"inherent":[18],"computation":[21],"of":[22,27,60,73,91,128,139,147,167,173,201],"stationary":[24,62,155],"performance":[25,63,117,156,175],"indices":[26,64,118,157],"large":[28],"stochastic":[29],"models.":[30],"The":[31,71],"method":[33],"is":[34,68,75,105],"based":[35,76],"on":[36,77,115,185],"a":[37,81,97,125,182],"aggregation":[39],"technique":[40],"and":[41,112,197],"applies":[42],"Markov":[44,82,103,189],"chains":[45],"exhibiting":[46],"some":[47,194],"structural":[48],"regularity.":[49],"Moreover,":[50],"it":[51,149],"allows":[52,150],"one":[53,151],"efficiently":[55],"compute":[56],"exact":[58,154],"values":[59],"when":[65],"model":[67],"actually":[69],"lumpable.":[70,106],"notion":[72,127,166],"quasi-lumpability":[74],"idea":[79],"that":[80,99],"chain":[83,104],"can":[84,119],"be":[85,120],"altered":[86],"by":[87],"relatively":[88],"small":[89],"perturbations":[90],"transition":[93],"rates":[94],"in":[95],"such":[96],"way":[98],"new":[101],"resulting":[102],"case,":[109],"only":[110],"upper":[111],"lower":[113],"bounds":[114],"derived.":[121],"Here,":[122],"introduce":[124,164],"novel":[126],"quasi-lumpability,":[129,148],"named":[130],"proportional":[131,168,183],",":[133],"which":[134],"extends":[135],"original":[137,160],"definition":[138,146],"but,":[141],"differently":[142],"from":[143],"general":[145],"derive":[153],"for":[158,170],"process.":[161],"We":[162],"then":[163],"bisimilarity":[169,180],"terms":[172],"process":[176],"algebra":[177],"PEPA.":[178],"Proportional":[179],"induces":[181],"underlying":[187],"continuous-time":[188],"chains.":[190],"Finally,":[191],"prove":[193],"compositionality":[195],"results":[196],"show":[198],"applicability":[200],"our":[202],"theory":[203],"through":[204],"examples.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2021-07-05T00:00:00"}
