Characterization of Single Cycle CA and its Application in Pattern Classification

The special class of irreversible cellular automaton (CA) with multiple attractors is of immense interest to the CA researchers. Characterization of such a CA is the necessity to devise CA based solutions for diverse applications. This work explores the essential properties of CA attractors towards characterization of the 1-dimensional cellular automata with point states (single length cycle attractors). The concept of Reachability Tree is introduced for such characterization. It enables identification of the pseudo-exhaustive bits (PE bits) of a CA defining its point states. A theoretical framework has been developed to devise schemes for synthesizing a single length cycle multiple attractor CA with the specific set of PE bits. It also results in a linear time solution while synthesizing a CA for the given set of attractors and its PE bits. The experimentation establishes that the proposed CA synthesis scheme is most effective in designing the efficient pattern classifiers for wide range of applications.