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Due to lack of efficient algebraic tools, the stability of multi\u2010valued NFSRs has been much less studied. This paper studies the stability of multi\u2010valued NFSRs using a logic network approach. A multi\u2010valued NFSR can be viewed as a logic network. Based on its logic network representation, some sufficient and necessary conditions are provided for globally (locally) stable multi\u2010valued NFSRs, explicit forms are given for the set of basins, and the algorithm for obtaining the set of basins is provided as well. Finally, a new method is presented for constructing stable <jats:italic>n<\/jats:italic> + 1\u2010stage NFSRs from stable <jats:italic>n<\/jats:italic>\u2010stage NFSRs by the properties of <jats:italic>D<\/jats:italic>\u2010morphism.<\/jats:p>","DOI":"10.1155\/2019\/8765970","type":"journal-article","created":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T23:36:33Z","timestamp":1550792193000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Stability of Multi\u2010Valued Nonlinear Feedback Shift Registers"],"prefix":"10.1155","volume":"2019","author":[{"given":"Haiyan","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2415-0401","authenticated-orcid":false,"given":"Qiuzhen","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6203-1254","authenticated-orcid":false,"given":"Jianyong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2208-962X","authenticated-orcid":false,"given":"Jianqiang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianghua","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongdai","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1201-8051","authenticated-orcid":false,"given":"Lijia","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,2,21]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1964.1053678"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1966.264498"},{"key":"e_1_2_9_3_2","unstructured":"MowleF. 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