Related papers: Commutative automata networks
We state an algorithm that, given an automata network and a block-sequential update schedule, produces an automata network of the same size or smaller with the same limit dynamics under the parallel update schedule. Then, we focus on the…
This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…
We settle the theoretical ground for the study of automata networks under block-parallel update schedules, which are somehow dual to the block-sequential ones, but allow for repetitions of automaton updates. This gain in expressivity brings…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
A \beta-skeleton is a proximity undirected graph whose connectivity is determined by the parameter \beta. We study \beta-skeleton automata where every node is a finite state machine taking two states, and updating its states depending on…
Automata networks, and in particular Boolean networks, are used to model diverse networks of interacting entities. The interaction graph of an automata network is its most important parameter, as it represents the overall architecture of…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
A variety of modeling frameworks have been proposed and utilized in complex systems studies, including dynamical systems models that describe state transitions on a system of fixed topology, and self-organizing network models that describe…
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…
Recently we have used a cellular automata model which describes the dynamics of a multi-connected network to reproduce the refractory behavior and aging effects obtained in immunization experiments performed with mice when subjected to…
The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
This paper details a method for optimising the size of Boolean automata networks in order to compute their attractors under the parallel update schedule. This method relies on the formalism of modules introduced recently that allows for…
In this paper we initiate the study of cellular automata on racks. A rack $R$ is a set with a self-distributive binary operation. The rack $R$ acts on the set $A^R$ of configurations from $R$ to a set $A$. We define the cellular automaton…
Cellular automata are topological dynamical systems. We consider the problem of deciding whether two cellular automata are conjugate or not. We also consider deciding strong conjugacy, that is, conjugacy by a map that commutes with the…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…