Search Results (3 total)

Classifying the initial configuration of a binary-state cellular automaton (CA) as to whether it contains a majority of 0s or 1s—the so-called density-classification problem—has been studied over the past decade by researchers wishing to glean an understanding of how locally interacting systems compute global properties. In this paper we prove two necessary conditions that a CA must satisfy in order to classify density: (1) the density of the initial configuration must be conserved over time, and (2) the rule table must exhibit a density of 0.5.

Recently, there has been a resurgence of interest in the use of cellular automata (CA) as computational devices. This paper demonstrates the advantages of nonuniform CAs, in which cellular rules may be heterogeneous, over the classical, uniform model. We address three problems that require global computation: parity, symmetry, and synchronization, showing that: (1) there does not exist a uniform, radius r=1 CA that effectively computes a solution, while (2) construction of a nonuniform CA is straightforward.

It has recently been shown that no one-dimensional, two-state cellular automaton can classify binary strings according to whether their density of 1s exceeds 0.5 or not. We show that by changing the output specification, namely, the final pattern toward which the system should converge, without increasing its computational complexity, a two-state, r  =  1 cellular automaton exists that can perfectly solve the density problem.