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This investigation studies nonemptiness problems of plane edge coloring with three colors. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges that have one of p colors are arranged side by side such that the touching edges of the adjacent tiles have the same colors. Given a basic set B of Wang tiles, the nonemptiness problem is to determine whether or not Σ(B)≠∅, where...
This study investigates the complexity of the global set of output patterns for two-dimensional multi-layer cellular neural networks. Applying labeling to the output space produces a two-dimensional sofic shift space. The ordering matrices and symbolic transition matrices are introduced to study the spatial entropy of the output space.
This talk is concerned with zeta functions of two-dimensional shifts of finite type. The zeta function is an important invariant, which combines information of all periodic patterns. The zeta function can be explicitly expressed as a reciprocal of an infinite product of polynomials by patterns generation approaches. The methods can apply to two-dimensional cellular neural networks.
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