On the Cell-based Complexity of Recognition of Bounded Configurations by Finite Dynamic Cellular Automata

TL;DR

This paper investigates the complexity involved in recognizing bounded configurations using finite dynamic cellular automata, exploring how layered automata can improve recognition efficiency for certain practical problems.

Contribution

It introduces a formal model for recognition complexity in FDCA and identifies conditions where layered automata outperform single-layer models.

Findings

Layered automata can recognize certain classes of configurations more efficiently.

Derived complexity measures help identify when multi-layered automata are beneficial.

Practical recognition problems can satisfy the proposed conditions.

Abstract

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and computer vision, this study attempts to derive the properties of a complexity measure and of the classes of input configurations that make it beneficial to realize the recognition via a two-layered automaton as compared to a one-layered automaton. A formalized model of an image pattern recognition task is utilized to demonstrate that the derived conditions can be satisfied for a non-empty set of practical problems.