相关论文: Dualities for Multi-State Probabilistic Cellular A…

Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are…

From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the…

We will consider a family of cellular automata $\Phi: \{1,2,...,r\}^\mathbb{N}\circlearrowright$ that are not of algebraic type. Our first goal is to determine conditions that result in the identification of probabilities that are at the…

This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA…

Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…

We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…

We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.

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…

This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…

In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…

We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N \geq 2$) synchronous dynamics on $S^{\mathbb Z^d}$(PCA). Increasing means the coupling preserves stochastic ordering. We first present our…

Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…

Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…

Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the…

We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the posterior distribution. The peculiar feature of PCA is their…

Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…