Abstract
This paper studies a special class of non-uniform cellular automata (CAs) that contain only single length cycle (point) attractors in their state space. These CAs always converge to some point attractors. A number of theorems and lemmas are reported in this paper to characterize this class of CAs. Reachability tree, a discrete tool for characterizing 1-d CA, has been utilized to develop theories for these types of CAs. We finally report an algorithm that synthesizes a non-uniform cellular automaton having only point attractors.
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