{"id":"https://openalex.org/W2996117690","doi":"https://doi.org/10.1145/3371923","title":"A Lyapunov Approach for Time-Bounded Reachability of CTMCs and CTMDPs","display_name":"A Lyapunov Approach for Time-Bounded Reachability of CTMCs and CTMDPs","publication_year":2020,"publication_date":"2020-02-04","ids":{"openalex":"https://openalex.org/W2996117690","doi":"https://doi.org/10.1145/3371923","mag":"2996117690"},"language":"en","primary_location":{"id":"doi:10.1145/3371923","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3371923","pdf_url":null,"source":{"id":"https://openalex.org/S4210231956","display_name":"ACM Transactions on Modeling and Performance Evaluation of Computing Systems","issn_l":"2376-3639","issn":["2376-3639","2376-3647"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Performance Evaluation of Computing 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/A5025105412","display_name":"Mahmoud Salamati","orcid":"https://orcid.org/0000-0003-3790-3935"},"institutions":[{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mahmoud Salamati","raw_affiliation_strings":["MPI-SWS, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI-SWS, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I4210121786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017334634","display_name":"Sadegh Soudjani","orcid":"https://orcid.org/0000-0003-1922-6678"},"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":false,"raw_author_name":"Sadegh Soudjani","raw_affiliation_strings":["Newcastle University, Newcastle upon Tyne, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Newcastle University, Newcastle upon Tyne, United Kingdom","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081010207","display_name":"Rupak Majumdar","orcid":"https://orcid.org/0000-0003-2136-0542"},"institutions":[{"id":"https://openalex.org/I4210121786","display_name":"Max Planck Institute for Software Systems","ror":"https://ror.org/02pe2kf23","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210121786"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rupak Majumdar","raw_affiliation_strings":["MPI-SWS, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI-SWS, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I4210121786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025105412"],"corresponding_institution_ids":["https://openalex.org/I4210121786"],"apc_list":null,"apc_paid":null,"fwci":0.1458,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.49205026,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":"1","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","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/T10142","display_name":"Formal Methods in Verification","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/T11125","display_name":"Petri Nets in System Modeling","score":0.9979000091552734,"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/T12423","display_name":"Software Reliability and Analysis Research","score":0.9945999979972839,"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/mathematics","display_name":"Mathematics","score":0.6261494159698486},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5818558931350708},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.5571978688240051},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5531392097473145},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5449884533882141},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4925006330013275},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4842934012413025},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4569052755832672},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.453523725271225},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3394218683242798},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14369413256645203},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1317349672317505},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12252435088157654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6261494159698486},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5818558931350708},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.5571978688240051},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5531392097473145},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5449884533882141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4925006330013275},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4842934012413025},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4569052755832672},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.453523725271225},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3394218683242798},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14369413256645203},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1317349672317505},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12252435088157654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3371923","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3371923","pdf_url":null,"source":{"id":"https://openalex.org/S4210231956","display_name":"ACM Transactions on Modeling and Performance Evaluation of Computing Systems","issn_l":"2376-3639","issn":["2376-3639","2376-3647"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Performance Evaluation of Computing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7099999785423279,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1760551737","https://openalex.org/W1781946001","https://openalex.org/W1968402813","https://openalex.org/W1976268573","https://openalex.org/W2015172530","https://openalex.org/W2019214951","https://openalex.org/W2020204292","https://openalex.org/W2041226400","https://openalex.org/W2076420009","https://openalex.org/W2113642685","https://openalex.org/W2121117794","https://openalex.org/W2141881497","https://openalex.org/W2165748475","https://openalex.org/W2262106677","https://openalex.org/W2518771331","https://openalex.org/W2536620281","https://openalex.org/W2610857016","https://openalex.org/W2885972047","https://openalex.org/W3210839039","https://openalex.org/W4300353561"],"related_works":["https://openalex.org/W2331587294","https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W1990502710","https://openalex.org/W2159479095","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062"],"abstract_inverted_index":{"Time-bounded":[0],"reachability":[1,226],"is":[2,39,99],"a":[3,31,44,49,93,100,144,164,211,230,271],"fundamental":[4],"problem":[5],"in":[6,20,107,160],"model":[7],"checking":[8],"continuous-time":[9],"Markov":[10,14],"chains":[11],"(CTMCs)":[12],"and":[13,47,120],"decision":[15],"processes":[16],"(CTMDPs)":[17],"for":[18,153,204,213,255],"specifications":[19],"continuous":[21],"stochastic":[22],"logics.":[23],"It":[24],"can":[25,157],"be":[26,158],"computed":[27,159],"by":[28,181],"numerically":[29,65],"solving":[30,66],"characteristic":[32],"linear":[33],"dynamical":[34,55,69,179,207],"system,":[35],"but":[36,265],"the":[37,67,75,78,105,108,111,117,127,138,151,154,168,177,183,190,214,224,239,244,248,275],"procedure":[38],"computationally":[40],"expensive.":[41],"We":[42,209,232,246],"take":[43],"control-theoretic":[45],"approach":[46,198],"propose":[48],"reduction":[50],"technique":[51,86,249,267],"that":[52,64,114,150,221,223,236],"finds":[53],"another":[54],"system":[56,70,80,180,220],"of":[57,61,77,104,110,167,185,243,274],"lower":[58],"dimension":[59],"(number":[60],"variables),":[62],"such":[63],"reduced":[68,155,178,191,272],"provides":[71],"an":[72,134,186],"approximation":[73],"to":[74,92,132,174],"solution":[76],"original":[79],"with":[81],"guaranteed":[82],"error":[83,135,234],"bounds.":[84],"Our":[85,96],"generalizes":[87],"lumpability":[88,257],"(or":[89],"probabilistic":[90],"bisimulation)":[91],"quantitative":[94],"setting.":[95],"main":[97],"result":[98],"Lyapunov":[101,128,202],"function":[102,129],"characterization":[103],"difference":[106],"trajectories":[109],"two":[112,139],"dynamics":[113,140,156],"depends":[115],"on":[116,238,250],"initial":[118],"mismatch":[119],"exponentially":[121],"decreases":[122],"over":[123],"time.":[124],"In":[125],"particular,":[126],"enables":[130,172],"us":[131,173],"compute":[133],"bound":[136],"between":[137],"as":[141,143],"well":[142],"convergence":[145],"rate.":[146],"Finally,":[147],"we":[148,195],"show":[149],"search":[152],"polynomial":[161],"time":[162,242],"using":[163,199,270],"Schur":[165],"decomposition":[166],"transition":[169],"matrix.":[170],"This":[171],"efficiently":[175],"solve":[176],"computing":[182],"exponential":[184],"upper-triangular":[187],"matrix":[188],"characterizing":[189],"dynamics.":[192],"For":[193],"CTMDPs,":[194],"generalize":[196],"our":[197,266],"piecewise":[200],"quadratic":[201],"functions":[203],"switched":[205,219],"affine":[206],"systems.":[208],"synthesize":[210],"policy":[212],"CTMDP":[215],"via":[216],"its":[217],"reduced-order":[218],"guarantees":[222],"time-bounded":[225],"probability":[227],"lies":[228],"above":[229],"threshold.":[231],"provide":[233],"bounds":[235],"depend":[237],"minimum":[240],"dwell":[241],"policy.":[245],"demonstrate":[247],"examples":[251],"from":[252],"queueing":[253],"networks,":[254],"which":[256],"does":[258],"not":[259],"produce":[260],"any":[261],"state":[262],"space":[263],"reduction,":[264],"synthesizes":[268],"policies":[269],"version":[273],"model.&lt;?vsp":[276],"-2pt?&gt;":[277]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
