Related papers: A categorical framework for cellular automata
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
In this paper, we propose a new text categorization framework based on Concepts Lattice and cellular automata. In this framework, concept structure are modeled by a Cellular Automaton for Symbolic Induction (CASI). Our objective is to…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
This is a major update of the previous version. The methods of the paper are now fully constructive and the style is "formalization ready" with the emphasis on the possibility of formalization both in type theory and in constructive set…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
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…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
We develop fibrational perspectives on context-free grammars and on nondeterministic finite-state automata over categories and operads. A generalized CFG is a functor from a free colored operad (aka multicategory) generated by a pointed…
We study the most elementary family of cellular automata defined over an arbitrary group universe $G$ and an alphabet $A$: the lazy cellular automata, which act as the identity on configurations in $A^G$, except when they read a unique…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group. Like the usual automatic groups graph automatic ones enjoy…