{"id":"https://openalex.org/W3116681538","doi":"https://doi.org/10.1142/s0218194022500103","title":"Formal Modeling and Performance Evaluation for Hybrid Systems: A Probabilistic Hybrid Process Algebra-Based Approach","display_name":"Formal Modeling and Performance Evaluation for Hybrid Systems: A Probabilistic Hybrid Process Algebra-Based Approach","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W3116681538","doi":"https://doi.org/10.1142/s0218194022500103","mag":"3116681538"},"language":"en","primary_location":{"id":"doi:10.1142/s0218194022500103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218194022500103","pdf_url":null,"source":{"id":"https://openalex.org/S131442419","display_name":"International Journal of Software Engineering and Knowledge Engineering","issn_l":"0218-1940","issn":["0218-1940","1793-6403"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Software Engineering and Knowledge Engineering","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/A5100717597","display_name":"Fujun Wang","orcid":"https://orcid.org/0000-0001-9902-3859"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fujun Wang","raw_affiliation_strings":["College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017248361","display_name":"Zining Cao","orcid":"https://orcid.org/0000-0002-4673-200X"},"institutions":[{"id":"https://openalex.org/I4210120442","display_name":"AVIC Optronics (China)","ror":"https://ror.org/0338ntq56","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210120442"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zining Cao","raw_affiliation_strings":["Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","Key Laboratory of Safety-Critical Software, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","Science and Technology on Electro-optic Control Laboratory, Luoyang 471000, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Key Laboratory of Safety-Critical Software, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Science and Technology on Electro-optic Control Laboratory, Luoyang 471000, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210120442"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045326313","display_name":"Lixing Tan","orcid":"https://orcid.org/0000-0002-2978-2697"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lixing Tan","raw_affiliation_strings":["College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100332568","display_name":"Zhen Li","orcid":"https://orcid.org/0000-0002-0001-2998"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Li","raw_affiliation_strings":["College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017248361"],"corresponding_institution_ids":["https://openalex.org/I4210120442","https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.1437,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42588621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"02","first_page":"283","last_page":"315"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998000264167786,"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/T10142","display_name":"Formal Methods in Verification","score":0.9998000264167786,"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/T11005","display_name":"Radiation Effects in Electronics","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.9173475503921509},{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.8705083131790161},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.8529374599456787},{"id":"https://openalex.org/keywords/probabilistic-argumentation","display_name":"Probabilistic argumentation","score":0.6653599739074707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.603525698184967},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5246391892433167},{"id":"https://openalex.org/keywords/process-calculus","display_name":"Process calculus","score":0.524359941482544},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5183680653572083},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5123549699783325},{"id":"https://openalex.org/keywords/transition-system","display_name":"Transition system","score":0.4772469997406006},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.44814157485961914},{"id":"https://openalex.org/keywords/probabilistic-relevance-model","display_name":"Probabilistic relevance model","score":0.42772793769836426},{"id":"https://openalex.org/keywords/probabilistic-analysis-of-algorithms","display_name":"Probabilistic analysis of algorithms","score":0.40449023246765137},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3645957112312317},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2956913113594055},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14068293571472168}],"concepts":[{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.9173475503921509},{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.8705083131790161},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8529374599456787},{"id":"https://openalex.org/C128828806","wikidata":"https://www.wikidata.org/wiki/Q7246848","display_name":"Probabilistic argumentation","level":3,"score":0.6653599739074707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.603525698184967},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5246391892433167},{"id":"https://openalex.org/C161771561","wikidata":"https://www.wikidata.org/wiki/Q1970286","display_name":"Process calculus","level":2,"score":0.524359941482544},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5183680653572083},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5123549699783325},{"id":"https://openalex.org/C2779167558","wikidata":"https://www.wikidata.org/wiki/Q176468","display_name":"Transition system","level":2,"score":0.4772469997406006},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.44814157485961914},{"id":"https://openalex.org/C143017306","wikidata":"https://www.wikidata.org/wiki/Q3318133","display_name":"Probabilistic relevance model","level":4,"score":0.42772793769836426},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.40449023246765137},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3645957112312317},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2956913113594055},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14068293571472168},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218194022500103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218194022500103","pdf_url":null,"source":{"id":"https://openalex.org/S131442419","display_name":"International Journal of Software Engineering and Knowledge Engineering","issn_l":"0218-1940","issn":["0218-1940","1793-6403"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Software Engineering and Knowledge Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2032540946","display_name":null,"funder_award_id":"NJ20170007","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2226322849","display_name":null,"funder_award_id":"NJ2019010","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2821560599","display_name":null,"funder_award_id":"NJ2020022","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4238289496","display_name":"\u9ad8\u53ef\u4fe1\u5d4c\u5165\u5f0f\u8f6f\u4ef6\u5efa\u6a21\u4e0e\u9a8c\u8bc1\u65b9\u6cd5\u7684\u7814\u7a76","funder_award_id":"61572253","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6425954411","display_name":null,"funder_award_id":"20185152035","funder_id":"https://openalex.org/F4320327472","funder_display_name":"Chinese Aeronautical Establishment"},{"id":"https://openalex.org/G7979829608","display_name":null,"funder_award_id":"20150652008","funder_id":"https://openalex.org/F4320327472","funder_display_name":"Chinese Aeronautical Establishment"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327472","display_name":"Chinese Aeronautical Establishment","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W660320","https://openalex.org/W35751504","https://openalex.org/W47800957","https://openalex.org/W173641204","https://openalex.org/W258022877","https://openalex.org/W427198658","https://openalex.org/W1489359924","https://openalex.org/W1498125516","https://openalex.org/W1498432697","https://openalex.org/W1503973138","https://openalex.org/W1511105469","https://openalex.org/W1530657611","https://openalex.org/W1547304883","https://openalex.org/W1548324490","https://openalex.org/W1584244501","https://openalex.org/W1595871524","https://openalex.org/W1597181838","https://openalex.org/W1601373402","https://openalex.org/W1805131879","https://openalex.org/W1862398452","https://openalex.org/W1968437296","https://openalex.org/W1971947347","https://openalex.org/W2005998857","https://openalex.org/W2011979623","https://openalex.org/W2044667269","https://openalex.org/W2074833236","https://openalex.org/W2076006764","https://openalex.org/W2077815947","https://openalex.org/W2107471150","https://openalex.org/W2108886305","https://openalex.org/W2124778357","https://openalex.org/W2125614702","https://openalex.org/W2126489030","https://openalex.org/W2127452188","https://openalex.org/W2146596541","https://openalex.org/W2168821867","https://openalex.org/W2560421581","https://openalex.org/W2809681923","https://openalex.org/W2963576416","https://openalex.org/W3047659890","https://openalex.org/W3110927164","https://openalex.org/W3136666733","https://openalex.org/W3189981105","https://openalex.org/W4238893454","https://openalex.org/W4302769929"],"related_works":["https://openalex.org/W2399470155","https://openalex.org/W2129909535","https://openalex.org/W2136070637","https://openalex.org/W2167838019","https://openalex.org/W3210775325","https://openalex.org/W1554045856","https://openalex.org/W2171004374","https://openalex.org/W1997454380","https://openalex.org/W2362353803","https://openalex.org/W2494523064"],"abstract_inverted_index":{"Probabilistic":[0],"behavior":[1],"is":[2,52,80,83,179],"omnipresent":[3],"in":[4,7,57],"computer-controlled":[5],"systems,":[6,12],"particular,":[8],"so-called":[9],"safety-critical":[10],"hybrid":[11,32],"due":[13],"to":[14,116,157,160,181],"various":[15],"reasons,":[16],"like":[17],"uncertain":[18],"environments":[19],"or":[20,120],"fundamental":[21],"properties":[22],"of":[23,60,67,88,97,153,185],"nature.":[24],"In":[25],"this":[26,73,136],"paper,":[27],"we":[28,138],"extend":[29],"the":[30,42,58,64,68,86,95,150,167,183],"existing":[31,47],"process":[33],"algebra":[34],"ACP[Formula:":[35],"see":[36,155],"text]":[37,156],"with":[38],"probability":[39,99],"without":[40],"sacrificing":[41],"nondeterministic":[43],"choice":[44],"operator.":[45],"The":[46],"approximate":[48,77],"probabilistic":[49,78,106,163],"bisimulation":[50,79],"relation":[51],"fragile":[53],"and":[54,128],"not":[55,129],"robust":[56],"sense":[59],"being":[61],"dependent":[62],"on":[63],"deviation":[65,100],"range":[66,152],"transition":[69,98],"probability.":[70],"To":[71,134],"overcome":[72],"defect,":[74],"a":[75,140],"novel":[76],"proposed":[81],"which":[82],"inspired":[84],"by":[85,93],"idea":[87],"Probably":[89],"Approximately":[90],"Correct":[91],"(PAC)":[92],"relaxing":[94],"constraints":[96],"range.":[101],"Traditional":[102],"temporal":[103,107],"logics,":[104,108],"even":[105],"are":[109,114,125,173],"expressive":[110],"enough,":[111],"but":[112],"they":[113,124],"limited":[115],"producing":[117],"only":[118],"true":[119],"false":[121],"responses,":[122],"as":[123],"still":[126],"logics":[127],"suitable":[130],"for":[131,170],"performance":[132,142,171],"evaluation.":[133],"settle":[135],"problem,":[137],"present":[139],"new":[141],"evaluation":[143,172],"language":[144],"that":[145],"expands":[146],"quantitative":[147],"analysis":[148],"from":[149],"value":[151],"[Formula:":[154],"real":[158],"number":[159],"reason":[161],"over":[162],"systems.":[164],"After":[165],"that,":[166],"corresponding":[168],"algorithms":[169],"given.":[174],"Finally,":[175],"an":[176],"industrial":[177],"example":[178],"given":[180],"demonstrate":[182],"effectiveness":[184],"our":[186],"method.":[187]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
