Partial Symmetry in Cellular Automata Rule Vectors

This letter demonstrates a partial symmetry in the rule vectors ofone-dimensional linear hybrid cellular automata (CA). The symmetry wasdiscovered in the CA realizations of the minimal cost primitive polynomialspublished by Bardell (1992). This symmetry turns out to be a simple functionof the structure of the polynomials coefficients, though the proof of thisseems to be far from trivial. This letter presents the symmetry function,and outlines its proof.