A split-and-perturb decomposition of number-conserving cellular automata

Digital phagograms: predicting phage infectivity through a multilayer machine learning approach

“…Recently, a new mathematical tool to study number conservation of CAs was proposed in [33]. The main result of that paper, the decomposition theorem, states that the local rule of any number-conserving CA can be decomposed into two parts: a split function and a perturbation.…”

“…In this subsection, we present a short description of the mathematical tool, introduced in [33], that is very useful for studying number conservation. The theory presented in [33] is developed for the general case of an arbitrary state set Q ⊆ R and even an arbitrary dimension. In this paper, we consider only one dimension and the state set Q = {0, 1, .…”

“…. , k−1}, and for this reason the definitions and facts from [33] can be reformulated in a simpler way. We start with the definition of a split function.…”

“…. , k − 1} and the considered dimension is one to present a simpler version of the definitions and facts given in [33].…”

A New Structure of 2-State Number-Conserving Cellular Automata

“…The NCCA is widely used to the research of lattice gas, traffic flow, etc. [14], [18] and it has been continuously studied until recently [17].…”