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Erschienen in:
29.11.2019 | Original Article
A construction of simple and smaller-state real-time generator for exponential sequences
Erschienen in: Artificial Life and Robotics | Ausgabe 1/2020
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Abstract
A model of cellular automata (\({\mathrm {CA}}\)) is considered to be a well-studied non-linear model of complex systems in which an infinite one-dimensional array of finite state machines (cells) updates itself in a synchronous manner according to a uniform local rule. A sequence generation problem on the \({\mathrm {CA}}\)s was studied and many scholars proposed real-time sequence generation algorithms for a variety of non-regular sequences such as \(\{2^n \,|\,n = 1, 2, 3,\ldots \}\), prime, and Fibonacci sequences. In this paper, we show that sequence \(\{ k^n | n=1, 2, 3, \ldots \}\) can be generated in real-time by a k-state \({\mathrm {CA}}\), when \(k \ge 3\), and give a mathematical proof of the correctness of the implementation.