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題 名 | A Global Convergence Theorem in Boolean Algebra |
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作 者 | 侯瑞琳; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 14:3B 2010.06[民99.06] |
頁 次 | 頁1135-1144 |
分類號 | 313 |
關鍵詞 | Discrete iterations; Boolean contraction; Incidence matrix; Fixed point; Finite boolean algebras; |
語 文 | 英文(English) |
英文摘要 | Robert has established a global convergence theorem in {0, 1}n: If a map Fˆfrom {0, 1}n to itself is contracting relative to the boolean vector distance d, then there exists a positive integer p ≤ n such that Fˆp is constant. In other words, Fˆhas a unique fixed point ξ such that for any x in {0, 1}n , we have Fˆp(x)= ξ. The structure ({0, 1}, +, ·, −, 0, 1) may be regarded as the two-element boolean algebra. In this paper, this result is extended to any map F from the product X of n finite boolean algebras to itself. |
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