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Solution of the Boolean Markus–Yamabe Problem

✍ Scribed by Mau-Hsiang Shih; Juei-Ling Ho

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
244 KB
Volume
22
Category
Article
ISSN
0196-8858

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✦ Synopsis

The main point in the design of content addressable memory would be under what conditions the state possessing the total information can attract all other states in the phase of the system. The problem can be formulated as a global asymptotic stability problem of Boolean dynamical systems. In this article we give a complete answer to this global asymptotic stability problem. The conditions employed involve the Hamming distance on the phase space 0 1 n as well as the spectral condition on the Jacobian Boolean matrix of F 0 1 n → 0 1 n evaluated at each point of 0 1 n . This article furnishes a complete solution of the Boolean Markus-Yamabe problem.

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