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We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…
We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The…
The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson--Dirichlet process $\operatorname {PD}(\alpha,\theta)$. We obtain distributional results yielding exact forms…
This paper studies the problem of model-checking of probabilistic automaton and probabilistic one-counter automata against probabilistic branching-time temporal logics (PCTL and PCTL$^*$). We show that it is undecidable for these problems.…
We consider backward filtrations generated by processes coming from deterministic and probabilistic cellular automata. We prove that these filtrations are standard in the classical sense of Vershik's theory, but we also study them from…
Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…
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…
We present numerical and analytical results for a special kind of one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel automaton. It is shown that the phase boundary separating the active and the recently found…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We revisit closed-loop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of…
Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is…
Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…
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 provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a…
We reproduce apparently complex cellular automaton behaviour with simple partial differential equations as developed in (Keane 09). Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame…