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The factors contributing to the persistence and stability of life are fundamental for understanding complex living systems. Organisms are commonly challenged by harsh and fluctuating environments that are suboptimal for growth and…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
In the present work, a geometrical method to generate a two dimensional random walk by means of a bidimensional Cellular Automaton is presented. We illustrate it by means of Conway's Game of Life with periodical borders, with a large…
Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Evolution, the engine behind the survival and growth of life on Earth, operates through the population-based process of reproduction. Inspired by this principle, this paper formally defines a newly emerging problem -- the population-based…
The accumulation of adaptations in an open-ended manner during lifetime learning is a holy grail in reinforcement learning, intrinsic motivation, artificial curiosity, and developmental robotics. We present a specification for a cognitive…
Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. On the…
We prove the existence of a semilinear representation of Cellular Automata (CA) with the introduction of multiple convolution kernels. Examples of the technique are presented for rules akin to the "edge-of-chaos" including the Turing…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
This article surveys some theoretical aspects of Cellular Automata (CAs) research. In particular, we discuss on maximal length CA. An n-cell CA is a maximal length CA, if all the configurations except one form a single cycle. There is a…
"You never forget how to ride a bike", -- but how is that possible? The brain is able to learn complex skills, stop the practice for years, learn other skills in between, and still retrieve the original knowledge when necessary. The…
In nature, the process of cellular growth and differentiation has lead to an amazing diversity of organisms -- algae, starfish, giant sequoia, tardigrades, and orcas are all created by the same generative process. Inspired by the incredible…
Large Language Models (LLMs) exhibit remarkable capabilities in the hierarchical decomposition of complex tasks through semantic reasoning. However, their application in embodied systems faces challenges in ensuring reliable execution of…
The rapid advancement of generative models has empowered modern AI systems to comprehend and produce highly sophisticated content, even achieving human-level performance in specific domains. However, these models are fundamentally…
We exhaustively explore the reprogrammability capabilities and the intrinsic universality of the Cartesian product $P \times C$ of the space $P$ of all possible computer programs of increasing size and the space $C$ of all possible…
For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper,…
In this paper, we study a class of cellular automata (CA) called stable cellular automata (SCA) that preserve stability by reflection, modulo-recurrent, and richness. After applying these automata to Sturmian words, we determine some of…
We propose a general framework for interactively learning models, such as (binary or non-binary) classifiers, orderings/rankings of items, or clusterings of data points. Our framework is based on a generalization of Angluin's equivalence…