Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$

One-Dimensional Cellular Automata with Reflective Boundary Conditions and Radius Three

“…This denition is a natural generalization of particular 1D null boundary CAs. As a special case with p = 2 the structure and reversibility problem over binary elds is studied by del Rey and Sanchez et al in [1] and primitive elds is studied by Cinkir et al in [2] and Siap et al in [3], respectively. The approach of studying the algebraic structure and their reversibility property for this general case is generalized from [3].…”

Emergence of density dynamics by surface interpolation in elementary cellular automata

“…This paper is concerned with the analysis of elementary cellular automata with periodic boundary conditions in the terminology presented by [16,17].…”

Reversibility of general 1D linear cellular automata over the binary fieldZ2under null boundary conditions

“…There are also studies dealing with the reversibility problem of several kinds of particular rules, such as the hybrid elementary CA(ECA) 90/150 [29], ECA 150 [8,13] and the five-neighbor linear rule over finite state set Z p [7,31].…”

“…Transition matrix has been a useful tool for those special linear rules [2,7,[9][10][11][12]29,32,33], because for any 1D linear rule (or some 2D ones) with any given number of cells, there is a transition matrix whose reversibility is equivalent to that of the CA. However, this method has fundamental limitations since the matrix size is dependent on the number of cells: it is obviously unwise to calculate the determinant of the transition matrix for each cell number, instead, we hope to find an algorithm which can tell the relationship between the reversibility of the transition matrix and its size.…”