{"id":"https://openalex.org/W2525326051","doi":"https://doi.org/10.1142/s021819401650039x","title":"Counterexample Generation in Stochastic Model Checking Based on PSO Algorithm with Heuristic","display_name":"Counterexample Generation in Stochastic Model Checking Based on PSO Algorithm with Heuristic","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2525326051","doi":"https://doi.org/10.1142/s021819401650039x","mag":"2525326051"},"language":"en","primary_location":{"id":"doi:10.1142/s021819401650039x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819401650039x","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/A5102862727","display_name":"Yan Ma","orcid":"https://orcid.org/0009-0000-2525-0055"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"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","SG"],"is_corresponding":true,"raw_author_name":"Yan Ma","raw_affiliation_strings":["College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China","School of Computing, National University of Singapore, Singapore 117417, Singapore"],"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"School of Computing, National University of Singapore, Singapore 117417, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"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/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":"Zining Cao","raw_affiliation_strings":["College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030965346","display_name":"Liu Yang","orcid":"https://orcid.org/0000-0002-6015-6141"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I137056471","display_name":"Nanjing University of Finance and Economics","ror":"https://ror.org/031y8am81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137056471"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["College of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China","School of Computing, National University of Singapore, Singapore 117417, Singapore"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China","institution_ids":["https://openalex.org/I137056471"]},{"raw_affiliation_string":"School of Computing, National University of Singapore, Singapore 117417, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102862727"],"corresponding_institution_ids":["https://openalex.org/I165932596","https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":1.3939,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83778873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"07","first_page":"1117","last_page":"1143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991999864578247,"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":0.9991999864578247,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":0.9907000064849854,"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/counterexample","display_name":"Counterexample","score":0.9788303971290588},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5377419590950012},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48986098170280457},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.4811312258243561},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4652017056941986},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.43694132566452026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42986100912094116},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42578035593032837},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3379518985748291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19551685452461243},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06385129690170288}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9788303971290588},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5377419590950012},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48986098170280457},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.4811312258243561},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4652017056941986},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.43694132566452026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42986100912094116},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42578035593032837},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3379518985748291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19551685452461243},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06385129690170288}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819401650039x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819401650039x","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W103774727","https://openalex.org/W122180706","https://openalex.org/W132969391","https://openalex.org/W1504403751","https://openalex.org/W1512013481","https://openalex.org/W1529165591","https://openalex.org/W1541407177","https://openalex.org/W1549312786","https://openalex.org/W1588201901","https://openalex.org/W1820051232","https://openalex.org/W1871367359","https://openalex.org/W1888172192","https://openalex.org/W1889956542","https://openalex.org/W1926463588","https://openalex.org/W1978884755","https://openalex.org/W1985759744","https://openalex.org/W1987734880","https://openalex.org/W1998779352","https://openalex.org/W2005998857","https://openalex.org/W2029510805","https://openalex.org/W2041226400","https://openalex.org/W2047217912","https://openalex.org/W2054364230","https://openalex.org/W2088501121","https://openalex.org/W2100112273","https://openalex.org/W2101577148","https://openalex.org/W2117473144","https://openalex.org/W2118467147","https://openalex.org/W2119926658","https://openalex.org/W2125777958","https://openalex.org/W2126940339","https://openalex.org/W2127574686","https://openalex.org/W2131058166","https://openalex.org/W2135819212","https://openalex.org/W2141881497","https://openalex.org/W2145113795","https://openalex.org/W2156008373","https://openalex.org/W2158870716","https://openalex.org/W2205963248","https://openalex.org/W2410243683","https://openalex.org/W2543580944","https://openalex.org/W4242441073"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W2953113086","https://openalex.org/W1552191998","https://openalex.org/W2056825861","https://openalex.org/W4226455345","https://openalex.org/W2765989158","https://openalex.org/W2952737788","https://openalex.org/W4289687320","https://openalex.org/W925418074","https://openalex.org/W2119610731"],"abstract_inverted_index":{"Providing":[0],"counterexample":[1,24,53,101,116,189],"for":[2,100,117,188],"the":[3,19,46,83,86,94,123,146,149,185],"refutation":[4],"of":[5,12,85,148,163],"a":[6,30,75,108,173],"property":[7],"is":[8,17,49,66,89,98,166],"an":[9],"essential":[10],"feature":[11],"model":[13,27,56,119,193],"checking,":[14],"if":[15],"it":[16,43,65,88],"not":[18],"most":[20],"important.":[21],"However,":[22],"generating":[23,51,115],"in":[25,54,172,191],"stochastic":[26,55,118,192],"checking":[28,57],"needs":[29],"dedicated":[31],"algorithm.":[32],"It":[33,138],"usually":[34,90],"costs":[35],"too":[36],"much":[37],"time":[38],"and":[39,41,64,128,152],"memory,":[40],"sometimes":[42],"cannot":[44],"find":[45],"counterexample.":[47,137],"What":[48],"worse,":[50],"smallest":[52],"has":[58],"been":[59],"proved":[60],"to":[61,68,82,92,114,135,144,156],"be":[62,69],"NP-complete,":[63],"unlikely":[67],"efficiently":[70],"approximable.":[71],"Although":[72],"there":[73],"are":[74,80],"few":[76],"heuristic":[77,95,133,154],"methods":[78],"that":[79,179],"applied":[81],"construction":[84],"counterexample,":[87,127],"difficult":[91],"determine":[93],"function":[96],"which":[97],"critical":[99],"generating.":[102],"In":[103],"this":[104],"paper,":[105],"we":[106],"present":[107,186],"particle":[109],"swarm":[110],"optimization":[111],"(PSO)-based":[112],"approach":[113,165],"checking.":[120,194],"We":[121],"define":[122],"diagnostic":[124],"sub-graph":[125],"as":[126],"extend":[129],"PSO":[130],"algorithm":[131,181,187],"with":[132],"(HPSO)":[134],"generate":[136,157],"adopts":[139],"indirect":[140],"path":[141],"coding":[142],"scheme":[143],"expand":[145],"scope":[147],"search":[150],"space,":[151],"employs":[153],"operator":[155],"more":[158],"effective":[159],"path.":[160],"The":[161,176],"validity":[162],"our":[164],"illustrated":[167],"by":[168],"some":[169],"case":[170],"studies":[171],"prototype":[174],"tool.":[175],"experiments":[177],"show":[178],"HPSO":[180],"can":[182],"significantly":[183],"outperform":[184],"generation":[190]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}