Deterministic Computing Techniques for Perfect Density Classification

Abstract

The aim of this paper is to solve the density classification task (DCT), an extensively studied classical problem, using one-dimensional nonuniform Cellular Automata (CA) rules. A perfect solution of DCT requires searching for CA rules for binary strings of all possible lengths. But the generic problem is still open though the solution exists only for a specific fixed length CA. This paper provides two fundamental ideas to solve this problem in a better way. The first technique solves this problem using deterministic Turing machines which ultimately leads to generation of different CA rules under periodic boundary conditions. In the second technique, the existence of DCT solution by analyzing the state transition diagrams (STDs) of number conserving CA rules is investigated. The possibility of finding the exact solutions of DCT using Turing machine, STD and number conservation property of CA rules can be viewed as an improvement over the approximate solutions obtained by evolutionary techniques.