Related papers: Cellular Automata Can Reduce Memory Requirements o…
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,…
The computational paradigm represented by Cellular Neural/nonlinear Networks (CNN) and the CNN Universal Machine (CNN-UM) as a Cellular Wave Computer, gives new perspectives for computational physics. Many numerical problems and simulations…
This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…
Generative Modelling has become a promising use case for near term quantum computers. In particular, due to the fundamentally probabilistic nature of quantum mechanics, quantum computers naturally model and learn probability distributions,…
A popular way to accelerate the sampling of rare events in molecular dynamics simulations is to introduce a potential that increases the fluctuations of selected collective variables. For this strategy to be successful, it is critical to…
Microbiological systems evolve to fulfill their tasks with maximal efficiency. The immune system is a remarkable example, where self-non self distinction is accomplished by means of molecular interaction between self proteins and antigens,…
Since their inception at {\it Macy conferences} in later 1940s complex systems remain the most controversial topic of inter-disciplinary sciences. The term `complex system' is the most vague and liberally used scientific term. Using…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing), and in which the global…
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…
A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…
We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…
We propose and investigate a probabilistic model of sublinear-time one-dimensional cellular automata. In particular, we modify the model of ACA (which are cellular automata that accept if and only if all cells simultaneously accept) so that…
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…
Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In…
In this paper we provide an analytical study of the theory of multi-valued and fuzzy cellular automata where the fuzziness appears as the result of the application of an underlying multi-valued or continuous logic as opposed to standard…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
Reservoir Computing (RC) is an appealing approach in Machine Learning that combines the high computational capabilities of Recurrent Neural Networks with a fast and easy training method. Likewise, successful implementation of neuro-inspired…