Partial Symmetry in Cellular Automata Rule Vectors

Abstract

This letter demonstrates a partial symmetry in the rule vectors of one-dimensional linear hybrid cellular automata (CA). The symmetry was discovered in the CA realizations of the minimal cost primitive polynomials published by Bardell (1992). This symmetry turns out to be a simple function of the structure of the polynomial‘s coefficients, though the proof of this seems to be far from trivial. This letter presents the symmetry function, and outlines its proof.