Set of periods of additive cellular automata

Set of periods of additive cellular automata

It is shown that the set of periods of any additive cellular automata F, where the addition is done modulo a prime p, can be determined using some simple conditions on the coefficients in the linear expression of F. In particular, we establish that the set of periods has only four possibilities: {1,m} for some m where 1 m<p, N\{pm : m ∈ N}, N\{2pm : m ∈ N ∪ {0}} or the whole set N = {1, 2, 3, ....

Theory of Additive Cellular Automata

This paper reports the complete characterization of additive cellular automata (ACA) that employ xor and xnor logic as the next state function. Compared to linear cellular automata (LCA) [3], which employs only xor logic in its next state function, an ACA display much wider varieties of state transition behavior and enhanced computing power. An analytical framework is developed to characterize ...

Decomposition of Additive Cellular Automata

Finite additive cellular automata with fixed and periodic boundary conditions are considered as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. Generalized eigenspace decomposition is determined and relevant cyclic subspaces are described in terms of symmetries. As an application, the...

Additive Cellular Automata and Algebraic Series

Additive Cellular Automata with External Inputs

In this paper we consider a form of cellular automata (CA) that allows for external input at each stage of it s evolut ion. The invest igat ion is carr ied out from an algebra ic viewp oint whereby the state st ructure of the CA, together with it s action, can be int erpret ed rin g-theoretically. Specifically, we conside r the st ruct ure of a t tract ors for different cont rols and the associ...