Related papers: Simulation Limitations of Affine Cellular Automata
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…
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…
Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by…
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…
A class of additive cellular automata (ACA) on a finite group is defined by an index-group $\m g$ and a finite field $\m F_p$ for a prime modulus $p$ \cite{Bul_arch_1}. This paper deals mainly with ACA on infinite commutative groups and…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…
We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Consider a finite set $A$ and an integer $n \geq 1$. This paper studies the concept of complete simulation in the context of semigroups of transformations of $A^n$, also known as finite state-homogeneous automata networks. For $m \geq n$, a…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…