This paper introduces a simple formalism for dealing with deterministic, nondeterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is not present in usual definitions. We show that this feature allows for strictly more behaviors (for instance, number conserving stochastic cellular automata r...

The cellular learning automata, which is a combination of cellular automata, and learning automata, is a new recently introduced model. This model is superior to cellular automata because of its ability to learn and is also superior to a single learning automaton because it is a collection of learning automata which can interact with each other. The basic idea of cellular learning automata, whi...

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stocha...

In this paper we present a model of the dynamics of an interesting class of stochastic cellular automata. Such automata are variants of automata used for density classification and they are chosen because they can be effectively used to address consensus problems. After introducing the topic and the basic notation, we study the dynamics of such automata by means of simulations with varying peri...

In this work we show an alternative form for forecasting trends in time series that behaves stochastically. For this, we are adopting a mathematical approach and treating the time series as the evolution of stochastic cellular automata, and thus, our problem narrows down to find the model for the cellular automata that best describes the behavior of time series. Using machine learning, more spe...

We show how some graph theoretical arguments may be used to reduce the complexity of the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from a Stochastic Automata Network (SAN). The structural properties of the automata are used to establish new various results. First, we establish the complexity of the resolutio...

To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.