Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We present a state of the art that covers the various approaches that deal with asynchronism in cellular automata and closely related models.Foreword: This article is the preprintof an article that is to appear in the Journal of cellular automata. It is an extended verion of the invited paper that appeared

In the density classification problem, a binary cellular automaton (CA) should decide whether an initial configuration contains more 0s or more 1s. The answer is given when all cells of the CA agree on a given state. This problem is known for having no exact solution in the case of binary deterministic one-dimensional CA. We investigate how randomness in CA may help us solve the problem. We analyse the behaviour of stochastic CA rules that perform the density classification task. We show that describing stochastic rules as a "blend" of deterministic rules allows us to derive quantitative results on the classification time and the classification time of previously studied rules. We introduce a new rule whose effect is to spread defects and to wash them out. This stochastic rule solves the problem with an arbitrary precision, that is, its quality of classification can be made arbitrarily high, though at the price of an increase of the convergence time. We experimentally demonstrate that this rule exhibits good scaling properties and that it attains qualities of classification never reached so far.

One of the main problems, which darkens the future of digital watermarking technologies, is the lack of detailed evaluation of existing marking schemes. This lack of benchmarking of current algorithms is blatant and confuses rights holders as well as software and hardware manufacturers and prevents them from using the solution appropriate to their needs. Indeed basing longlived protection schemes on badly tested watermarking technology does not make sense.In this paper we will present the architecture of a public automated evaluation service we have developed for still images, sound and video. We will detail and justify our choice of evaluation profiles, that is the series of tests applied to different types of watermarking schemes. These evaluation profiles allow us to measure the reliability of a marking scheme to different levels from low to very high.Beside the known StirMark transformations, we will also detail new tests that will be included in this platform. One of them is intended to measure the real size of the key space. Indeed, if one is not careful, two different watermarking keys may produce interfering watermarks and as a consequence the actual space of keys is much smaller than it appears. Another set of tests is related to audio data and addresses the usual equalisation and normalisation but also time stretching, pitch shifting. Finally we propose a set of tests for fingerprinting applications. This includes: averaging of copies with different fingerprint, random exchange of part between different copies and comparison between copies with selection of most/less frequently used position differences. NEED FOR EVALUATIONThe growing number of attacks against watermarking systems (e.g., 1, 2, 3 ) has shown that far more research is required to improve the quality of existing watermarking methods so that, for instance, the coming JPEG 2000 (and new multimedia standards) can be more widely used within electronic commerce applications.We already pointed out that most papers have used their own limited series of tests, their own pictures and their own methodology and that consequently comparison was impossible without re-implementing the method and trying to test them separately 4 . But then, the implementation might be very different and probably weaker than the one of the original authors. This led to suggest that methodologies for evaluating existing watermarking algorithms were urgently required and we proposed a simple benchmark for still image marking algorithms.With a well-defined benchmark, researchers and watermarking software manufacturers would just need to provide a table of results, which would give a good and reliable summary of the performances of the proposed scheme. So end users can check whether their basic requirements are satisfied. Researchers can compare different algorithms and see how a method can be improved or whether a newly added feature actually improves the reliability of the whole method. As far as the industry is concerned, risks can be properly associated with the ...

In this paper we propose a probabilistic analysis of the fully asynchronous behavior (i.e., two cells are never simultaneously updated, as in a continuous time process) of elementary finite cellular automata (i.e., {0, 1} states, radius 1 and unidimensional) for which both states are quiescent (i.e., (0, 0, 0) → 0 and (1, 1, 1) → 1). It has been experimentally shown in previous works that introducing asynchronism in the global function of a cellular automata was perturbing its behavior, but as far as we know, only few theoretical work exists on the subject. The cellular automata we consider live on a ring of size n and asynchronism is introduced as follows: at each time step one cell is selected uniformly at random and the transition is made on this cell while the others stay in the same state. Among the sixty-four cellular automata belonging to the class we consider, we show that nine of them diverge almost surely on all non-trivial configurations while the fifty-five other converge almost surely to a random fixed point. We show that the exact convergence time of these fifty-five automata can only take the following values: either 0, Θ(n ln n), Θ(n 2), Θ(n 3), or Θ(n2 n). Furthermore, the global behavior of each of these cellular automata is fully determined by reading its code.

In this paper we will briefly present the architecture of a public automated evaluation service we are developing for still images, sound and video.We will also detail new tests that will be included in this platform. The set of tests is related to audio data and addresses the usual equalisation and normalisation but also time stretching, pitch shifting and specially designed audio attack algorithms. These attacks are discussed and results on watermark attacks and perceived quality after applying the attacks are provided.

The decentralised gathering problem consists in grouping in a compact cluster agents that are initially randomly scattered. We propose a bio-inspired algorithm, the Reaction-Diffusion-Chemotaxis aggregation scheme, to group agents that have limited abilities. The agents and their environment are described with a stochastic model inspired by the aggregation of the Dictyostelium discoideum cellular slime mold. The environment is an active lattice, whose cells transmit information according to a reaction-diffusion mechanism. The agents are virtual amoebae; they trigger excitations randomly and move by following reaction-diffusion waves. We demonstrate that despite its simplicity, this model exhibits interesting properties of self-organisation and is efficient for gathering agents. Moreover, observations show that the system is robust to various perturbations, such as the presence of obstacles on the lattice or noise in the movements of the agents.

In this paper we propose a probabilistic analysis of the asynchronous behavior of elementary finite cellular automata (i.e. {0, 1} states, radius 1 and unidimensional) for which both states are quiescent (i.e. (0, 0, 0) → 0 and (1, 1, 1) → 1). It has been experimentally shown in previous works that introducing asynchronism in the global function of a cellular automata was perturbing its behavior, but as far as we know, only few theoretical work exists on the subject. The cellular automata we consider live on a ring of size n and asynchronism is introduced as follow: at each time step one cell is selected uniformly at random and the transition is made on this cell while the others stay in the same state. Under these conditions, we prove that the considered cellular automata can be classified relatively to their expected convergence time: Among the sixty-four cellular automata belonging to the class we consider, we show that nine of them diverge on all non-trivial configurations while the fifty five other always converge to a fixed point. We then study the convergence time of these fifty five automata and show that it can only take the following values: either 0, Θ(n ln n), Θ(n 2), Θ(n 3), or Ω(n2 n). More than that, we prove that the global behavior of any of these cellular automata is fully determined by reading its code. We end the paper by showing how some of these results can be extended to another kind of asynchronism in which at each time step, each cell has independently the same fixed probability to make its transition.

Typically viewed as a deterministic model of spatial computing, cellular automata are here considered as a collective system subject to the noise inherent to natural computing. The classical updating scheme is replaced by stochastic versions which either randomly update cells or disrupt the cell-to-cell transmission of information. We then use the novel updating schemes to probe the behaviour of Elementary Cellular Automata, and observe a wide variety of results. We study these behaviours in the scope of macroscopic statistical phenomena and microscopic analysis. Finally, we discuss the possibility to use updating schemes to probe the robustness of complex systems.