3,341 research outputs found
On the Parity Problem in One-Dimensional Cellular Automata
We consider the parity problem in one-dimensional, binary, circular cellular
automata: if the initial configuration contains an odd number of 1s, the
lattice should converge to all 1s; otherwise, it should converge to all 0s. It
is easy to see that the problem is ill-defined for even-sized lattices (which,
by definition, would never be able to converge to 1). We then consider only odd
lattices.
We are interested in determining the minimal neighbourhood that allows the
problem to be solvable for any initial configuration. On the one hand, we show
that radius 2 is not sufficient, proving that there exists no radius 2 rule
that can possibly solve the parity problem from arbitrary initial
configurations. On the other hand, we design a radius 4 rule that converges
correctly for any initial configuration and we formally prove its correctness.
Whether or not there exists a radius 3 rule that solves the parity problem
remains an open problem.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Fitness landscape of the cellular automata majority problem: View from the Olympus
In this paper we study cellular automata (CAs) that perform the computational
Majority task. This task is a good example of what the phenomenon of emergence
in complex systems is. We take an interest in the reasons that make this
particular fitness landscape a difficult one. The first goal is to study the
landscape as such, and thus it is ideally independent from the actual
heuristics used to search the space. However, a second goal is to understand
the features a good search technique for this particular problem space should
possess. We statistically quantify in various ways the degree of difficulty of
searching this landscape. Due to neutrality, investigations based on sampling
techniques on the whole landscape are difficult to conduct. So, we go exploring
the landscape from the top. Although it has been proved that no CA can perform
the task perfectly, several efficient CAs for this task have been found.
Exploiting similarities between these CAs and symmetries in the landscape, we
define the Olympus landscape which is regarded as the ''heavenly home'' of the
best local optima known (blok). Then we measure several properties of this
subspace. Although it is easier to find relevant CAs in this subspace than in
the overall landscape, there are structural reasons that prevent a searcher
from finding overfitted CAs in the Olympus. Finally, we study dynamics and
performance of genetic algorithms on the Olympus in order to confirm our
analysis and to find efficient CAs for the Majority problem with low
computational cost
Evolutionary Synthesis of Cellular Automata
Synthesis of cellular automata is an important area of modeling and describing complex systems. Large amounts of combinations and candidate solutions render the usage of deterministic approaches impractical and thus nondeterministic optimization methods have to be employed. Two of the typical evolutionary approaches to synthesizing cellular automata are the evolution of a single automaton and a genetic algorithm that evolves a population of automata. The first approach, with addition of some heuristics, is known as the cellular programming algorithm. In this paper we address the second approach and develop a genetic algorithm that evolves a population of cellular automata. We test both approaches on the density classification task, which is one of the most widely studied computational problems in the context of evolving cellular automata. Comparison of the synthesized cellular automata demonstrates unexpected similarity of the evolved rules and comparable classification accuracy performance of both approaches
The identification of cellular automata
Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of
hybrid CA is introduced
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Mean-Field Theory of Meta-Learning
We discuss here the mean-field theory for a cellular automata model of
meta-learning. The meta-learning is the process of combining outcomes of
individual learning procedures in order to determine the final decision with
higher accuracy than any single learning method. Our method is constructed from
an ensemble of interacting, learning agents, that acquire and process incoming
information using various types, or different versions of machine learning
algorithms. The abstract learning space, where all agents are located, is
constructed here using a fully connected model that couples all agents with
random strength values. The cellular automata network simulates the higher
level integration of information acquired from the independent learning trials.
The final classification of incoming input data is therefore defined as the
stationary state of the meta-learning system using simple majority rule, yet
the minority clusters that share opposite classification outcome can be
observed in the system. Therefore, the probability of selecting proper class
for a given input data, can be estimated even without the prior knowledge of
its affiliation. The fuzzy logic can be easily introduced into the system, even
if learning agents are build from simple binary classification machine learning
algorithms by calculating the percentage of agreeing agents.Comment: 23 page
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