Related papers: On algebraic cellular automata
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…
While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility…
We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the…
In this note, we prove that an affine cellular algebra $A$ is semisimple if and only if the scheme associated to $A$ is reduced and 0-dimensional, and the bilinear forms with respect to all layers of $A$ are isomorphisms. Moreover, if the…
For the first time a mathematical object is presented - a reversible cellular Automaton - with many paradoxical qualities, the main ones among them are: a frequent quickly return to its original state, the presence of a large number of…
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a…
We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields. The…
In this paper, under certain conditions we consider two-dimensional cellular automata with the Moore neighborhood. Namely, the characterization of 2D linear cellular automata defined by the Moore neighborhood with some mixed boundary…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations. We use this condition for the classification of fermionic cellu- lar automata (FCA) on Cayley graphs of…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is not. We provide a new algorithm, based on algebro-geometric…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…
A cellular automaton with $n$ states may be used for construction of reversible second-order cellular automaton with $n^2$ states. Reversible cellular automata with hidden parameters discussed in this paper are generalization of such…
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…