Abstract
This paper shows the connection between information transmission in one-dimensional cellular space and the maximum invariant set of an automaton system. The classification of cellular spaces by their information transmission ability, posed by Nishio and Kobuchi, is discussed in detail. What we are concerned with are various conspicuous cut points which reduce their information transmission ability. The main result shows that such cut points of information transmission can be quite far from the origin (of the cellular space).
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