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Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
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…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…
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…
We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the…
We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding…
This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…
Cellular automata are discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…
Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems…
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…