Modeling of asynchronous cellular automata with fixed-point attractors for pattern classification

Abstract

This paper addresses a detail characterization of the one-dimensional two-state 3-neighborhood asynchronous cellular automata (ACA) having multiple fixed-point attractors with the target to model this class of CA for designing efficient pattern classifier. The cells of ACA are independent, and they are updated independently. When an ACA cell is updated, it reads the states of its neighbors and then updates its state following the state transition function. The ACA rules are characterized considering an arbitrary cell is updated in each time step. A theorem is designed for the identification of ACA with only fixed-point attractors. From this theorem we get 146 out of 256 ACA in two-state 3-neighborhood interconnection which always approach towards fixed-Point attractors. To identify individual fixed-point attractors, a directed graph, namely Fixed-point graph (FPG) is proposed. The FPG guides us to point out the ACA having multiple fixed-points attractors. There are 83 such ACA (out of 146 ACA with only fixed-point attractors) that are utilized to design efficient pattern classifier. Finally, the proposed classifier is tested with real-life data sets, and it is observed that the performance of the proposed ACA based classifier is always better than that of traditional CA based classifier and is also better than many other well-known pattern classifiers.