Non-deterministic density classification with diffusive probabilistic cellular automata

We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a probability proportional to the number of occupied sites in the neighborhood, while occupied sites become empty with a probability proportional to the number of empty sites in the neighborhood. The probability that all sites become eventually occupied is equal to the density of occupied sites in the initial string.Comment: 4 pages, 4 figure

Cellular automata and other cellular systems:design & evolution

Nature abounds in examples of cellular systems. From ant colonies to cellular tissues, from molecular systems to the human brain, cellularity seems to be the way Nature operates. The brain, surely one of the most complex objects to be found on earth, is the quintessence of a cellular system: a huge number of simple elements with an extremely high local connectivity and deprived of any sort of central control, giving rise to a rich global behavior. Cellular interactions thus seem to be the basis for complex phenomena, exhibiting qualities often missing in human artifacts : robustness, self-repair and, more generally, adaptability. The goal of this thesis is to answer the following question: "What may be computed in cellular systems ?". This question is far from obvious and implies many interrogations such as how to obtain the aforementioned qualities, how to program such systems, and, more fundamentally, what does computation mean in a cellular system. This thesis is mainly centered around the abstract and formal model of Cellular Automata. Through the study and the resolution of different tasks by means of evolution or mathematical demonstrations, I will show that it is not unreasonable to expect artificial systems to exhibit some of the qualities of natural systems, and that (guided) artificial evolution is surely the best approach to define the local behavior of elements which, when grouped as a cellular system, give rise to a desired global behavior. Above all, I will argue that truly emergent behavior in such designed systems is only a matter of perspective

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

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

Research plan for the PhD: Evolution of Ontogenic, Cellular Systems for Problem Solving

ystems lies in their complex programming. Their highly non-linear behaviour renders mathematical analysis of their global behaviour very difficult, thus leaving us without deterministic algorithms to master them. It has been shown by [9,10] that cellular automata and other cellular systems [6] could be successfully programmed using different forms of probabilistic algorithms, all based on the evolutionary paradigm. Evolutionary algorithms ( [2, 4, 8]) and specifically genetic programming [7] have proven Capcarr`ere, M. S., PhD Research Plan 2 to be successful at tackling hard combinatorial problem, with large search spaces. Our choice for our cell programming will be evolution. Nevertheless, there is no free lunch and evolution can be (and often is) computationally intensive. So while it is reasonable to evolve a solution valid for all instances of a problem, it should not be adapted just to only one particular size of the problem; our cellular solutions nee

A Statistical Study of a Class of Cellular Evolutionary Algorithms

Parallel evolutionary algorithms, over the past few years, have proven empirically worthwhile, but there seems to be a lack of understanding of their workings. In this paper we concentrate on cellular (fine-grained) models, our objectives being: (1) to introduce a suite of statistical measures, both at the genotypic and phenotypic levels, which are useful for analyzing the workings of cellular evolutionary algorithms; and (2) to demonstrate the application and utility of these measures on a specific example\u2014the cellular programming evolutionary algorithm. The latter is used to evolve solutions to three distinct (hard) problems in the cellular-automata domain: density, synchronization, and random number generation. Applying our statistical measures, we are able to identify a number of trends common to all three problems (which may represent intrinsic properties of the algorithm itself, as well as a host of problem-specific features. We find that the evolutionary algorithm tends to undergo a number of phases which we are able to quantitatively delimit. The results obtained lead us to believe that the measures presented herein may prove useful in the general case of analyzing fine-grained evolutionary algorithms