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2010 A GLOBAL CONVERGENCE THEOREM IN BOOLEAN ALGEBRA
Juei-Ling Ho
Taiwanese J. Math. 14(3B): 1135-1144 (2010). DOI: 10.11650/twjm/1500405910

Abstract

Robert has established a global convergence theorem in $\{0,1\}^{n}$: If a map $\hat{F}$ from $\{0,1\}^{n}$ to itself is contracting relative to the boolean vector distance $d$, then there exists a positive integer $p \leq n$ such that $\hat{F}^{p}$ is constant. In other words, $\hat{F}$ has a unique fixed point $\xi$ such that for any $x$ in $\{0,1\}^{n}$, we have $\hat{F}^{p}(x) = \xi$. The structure ($\{0,1\},+,\cdot,-,0,1$) 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.

Citation

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Juei-Ling Ho. "A GLOBAL CONVERGENCE THEOREM IN BOOLEAN ALGEBRA." Taiwanese J. Math. 14 (3B) 1135 - 1144, 2010. https://doi.org/10.11650/twjm/1500405910

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1207.94090
MathSciNet: MR2674601
Digital Object Identifier: 10.11650/twjm/1500405910

Subjects:
Primary: 05B20, 94C10

Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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