A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos"

On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.Comment: Submitted to Journal of Computation Science, Special Issue on Cellular Automata Application

Methodology for predicting and/or compensating the behavior of optical frequency comb

RESUMEN: Optical frequency comb spectrum can change its behavior due to temperature fluctuations, normal dispersion, and mechanical vibrations. Such limitations can affect the peak power and wavelength separation of comb lines. In the propagation through single−mode fiber, the linear and non−linear phenomena can modify spectral shape, phase shifts and flatness of spectrum. To find a strategy of compensation, the PhD thesis is focused on a prediction methodology based on fuzzy cellular automata, intuitionistic fuzzy sets and fuzzy entropy measures. The research work proposes a predictor called intuitionistic fuzzy cellular automata based on mean vector and a validation measure called general intuitionistic fuzzy entropy based on adequacy and non−adequacy. In the accomplished experiments, the method was used in three experiments: mode−locked lasers, cascaded intensity modulators−Mach Zehnder modulators, and microresonator ring. The obtained results showed that the power and phase distortions were reduced by using a pulse shaper, where the method was programmed. In addition, the stability and/or instability of spectrum were found for the microresonator ring

Proceedings of AUTOMATA 2011 : 17th International Workshop on Cellular Automata and Discrete Complex Systems

International audienceThe proceedings contain full (reviewed) papers and short (non reviewed) papers that were presented at the workshop

Proceedings of AUTOMATA 2010: 16th International workshop on cellular automata and discrete complex systems

International audienceThese local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full paper

Automata 2009 On the Relationship between Boolean and Fuzzy Cellular Automata

Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification ” of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper we are interested in the relationship between Boolean and fuzzy models and we analytically show, for the first time, the existence of a strong connection between them by focusing on two properties: density conservation and additivity. We begin by giving a probabilistic interpretation of our fuzzification which leads to two important results. First, it establishes an equivalence between convergent fuzzy CA and the mean field approximation on Boolean CA, an estimation of their asymptotic density. Second, we show that the density conservation property, extensively studied in the Boolean domain, is preserved in the fuzzy domain: a Boolean CA is density conserving if and only if the corresponding FCA is sum preserving. A similar result is established for another novel “spatial ” density conservation property. Finally, we prove an interesting parallel between additivity of Boolean CA and oscillation of the corresponding fuzzy CA around its fixed point. In fact, we show that a Boolean CA has a certain form of additivity if and only if the behavior of the corresponding fuzzy CA around its fixed point coincides with the Boolean behavior. These connections between the Boolean and the fuzzy models are the first formal proofs of a relationship between them. Keywords: Fuzzy cellular automata, density conservation, additivity