On Synthesis of Non-Uniform Cellular Automata Having Only Point Attractors
Sumit Adak, Nazma Naskar, Pradipta Maji and Sukanta Das
This paper studies a special class of non-uniform finite cellular automata (CAs) that contain only single length cycle (point) attractors in their state spaces. These CAs always converge to some point attractors from an arbitrary seed. A number of theorems and lemmas are reported in this paper to characterize this class of CAs. A discrete tool for characterizing 1-d CA, termed as Reachability Tree, has been utilized to develop theories for this type of CAs. We report an algorithm that synthesizes a non-uniform CA having only point attractors. This class of CAs are finally utilized to design an efficient pattern classifier.
Keywords: Single length cycle attractor (point attractor), multi-state attractor, reachability tree, link, cross link.