Related papers: Probabilistic cellular automata with local transit…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
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…
We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional…
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…
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…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose a new reversibility-preserving online Symmetric…
In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the…
Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1}, and all the cells evolve synchronously. The new content of a cell is randomly…
We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of A. Toom. They are defined as stochastic perturbations of cellular automata with a binary state space and a…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…
In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
We present a method for construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…
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,…