{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:11Z","timestamp":1740103691489,"version":"3.37.3"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T00:00:00Z","timestamp":1592956800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61862003","61761006","2018GXNSFDA281052"],"award-info":[{"award-number":["61862003","61761006","2018GXNSFDA281052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61862003","61761006","2018GXNSFDA281052"],"award-info":[{"award-number":["61862003","61761006","2018GXNSFDA281052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012547","name":"Natural Science Foundation of Guangxi Zhuang Autonomous Region","doi-asserted-by":"publisher","award":["61862003","61761006","2018GXNSFDA281052"],"award-info":[{"award-number":["61862003","61761006","2018GXNSFDA281052"]}],"id":[{"id":"10.13039\/100012547","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,6,24]]},"abstract":"<jats:p>In a multiprocessor system, as a key measure index for evaluating its reliability, diagnosability has attracted lots of attentions. Traditional diagnosability and conditional diagnosability have already been widely discussed. However, the existing diagnosability measures are not sufficiently comprehensive to address a large number of faulty nodes in a system. This article introduces a novel concept of diagnosability, called two-round diagnosability, which means that all faulty nodes can be identified by at most a one-round replacement (repairing the faulty nodes). The characterization of two-round <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>t<\/mml:mi><\/mml:math>-diagnosable systems is provided; moreover, several important properties are also presented. Based on the abovementioned theories, for the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>n<\/mml:mi><\/mml:math>-dimensional hypercube <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msub><mml:mrow><mml:mi>Q<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><\/mml:math>, we show that its two-round diagnosability is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msup><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>+<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:math>, which is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:math> times its classic diagnosability. Furthermore, a fault diagnosis algorithm is proposed to identify each node in the system under the PMC model. For <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:msub><mml:mrow><mml:mi>Q<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math>, we prove that the proposed algorithm is the time complexity of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>O<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>n<\/mml:mi><mml:msup><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2020\/9535818","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T23:31:57Z","timestamp":1593041517000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Two-Round Diagnosability Measures for Multiprocessor Systems"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1990-6780","authenticated-orcid":true,"given":"Jiarong","family":"Liang","sequence":"first","affiliation":[{"name":"School of Computer, Electronics and Information, and with Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning 530004, China"}]},{"given":"Qian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information, and with Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning 530004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4170-3103","authenticated-orcid":true,"given":"Changzhen","family":"Li","sequence":"additional","affiliation":[{"name":"School of Public Policy and Management, Guangxi University, Nanning 530004, China"}]}],"member":"311","reference":[{"doi-asserted-by":"publisher","key":"1","DOI":"10.1109\/pgec.1967.264748"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1093\/comjnl\/bxx057"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1016\/j.ins.2007.08.012"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1016\/j.ins.2010.12.011"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1109\/tnnls.2019.2905715"},{"doi-asserted-by":"publisher","key":"6","DOI":"10.1109\/access.2017.2672602"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1109\/tc.2015.2506562"},{"doi-asserted-by":"publisher","key":"8","DOI":"10.1155\/2018\/5745628"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1109\/access.2017.2773144"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.1016\/j.amc.2013.09.063"},{"doi-asserted-by":"publisher","key":"11","DOI":"10.1016\/j.ipl.2010.08.015"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1016\/j.jpdc.2004.02.002"},{"doi-asserted-by":"publisher","key":"13","DOI":"10.1007\/s11227-011-0620-6"},{"doi-asserted-by":"publisher","key":"14","DOI":"10.1007\/s11227-013-0883-1"},{"doi-asserted-by":"publisher","key":"15","DOI":"10.1016\/j.dam.2018.03.079"},{"doi-asserted-by":"publisher","key":"16","DOI":"10.1007\/s00521-019-04180-2"},{"doi-asserted-by":"publisher","key":"17","DOI":"10.1016\/j.ipl.2011.03.011"},{"doi-asserted-by":"publisher","key":"18","DOI":"10.1109\/tpds.2007.1022"},{"doi-asserted-by":"publisher","key":"19","DOI":"10.1109\/tc.2005.19"},{"doi-asserted-by":"publisher","key":"20","DOI":"10.1016\/j.ins.2019.04.027"},{"doi-asserted-by":"publisher","key":"21","DOI":"10.1016\/j.ipl.2004.09.011"},{"doi-asserted-by":"publisher","key":"22","DOI":"10.1016\/j.tcs.2015.10.030"},{"doi-asserted-by":"publisher","key":"23","DOI":"10.1109\/tc.2013.228"},{"doi-asserted-by":"publisher","key":"24","DOI":"10.1080\/00207160500113173"},{"doi-asserted-by":"publisher","key":"25","DOI":"10.1080\/00207160.2011.638978"},{"doi-asserted-by":"publisher","key":"26","DOI":"10.1109\/tnnls.2013.2281663"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9535818.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9535818.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/9535818.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T23:32:00Z","timestamp":1593041520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/9535818\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,24]]},"references-count":26,"alternative-id":["9535818","9535818"],"URL":"https:\/\/doi.org\/10.1155\/2020\/9535818","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,6,24]]}}}