On Polynomial Rings in Information Dynamics of Linear CA
Fritz Von Haeseler and Hidenosuke Nishio
In this study of information dynamics we are considering linear cellular automata (CA) with states in the ring of maps from a finite field in itself. Since CA is linear we will utilize the formal Laurent series and polynomials, with particular interest in the structure of the subrings generated by the coefficients of powers of polynomials. We present results on the equality of these subrings together with an upper bound on the number of different subrings generated by linear CA. Upon those results, we present a recovery theorem which allows to compute the information contained in the initial configuration from a knowledge of the t-th iteration of CA map to the initial configuration.