Abstract
Asynchronous iterations have long been used in distributed computing algorithms to produce calculation methods that are potentially faster than a serial or parallel approach, but whose convergence is more difficult to demonstrate. Conversely, over the past decade, the study of the complex dynamics of asynchronous iterations has been initiated and deepened, as well as their use in computer security and bioinformatics. The first work of these studies focused on chaotic discrete dynamical systems, and links were established between these dynamics on the one hand, and between random or complex behaviours in the sense of the theory of the same name. Computer security applications have focused on pseudo-random number generation, hash functions, hidden information, and various security aspects of wireless sensor networks. At the bioinformatics level, this study of complex systems has allowed an original approach to understanding the evolution of genomes and protein folding. These various contributions are detailed in this review article, which is an extension of the paper “An update on the topological properties of asynchronous iterations” presented during the Sixth International Conference on Parallel, Distributed, GPU and Cloud Computing (Pareng 2019).
Highlights
In the context of distributed computing, serial and parallel approaches have very quickly shown their limitations, especially in terms of speed [1,2,3]
To finish with the introduction of this model, that the above Hypotheses Hypothesis 2 (H2) and Hypothesis 3 (H3) find their natural justification in the fact that the initiators of this theory were exclusively seeking the convergence of asynchronous iterations
This section focus on the presentation of various realizations of pseudorandom number generators based on asynchronous iterations, see Figure 1 for speed comparison
Summary
In the context of distributed computing, serial and parallel approaches have very quickly shown their limitations, especially in terms of speed [1,2,3]. Various approaches have been proposed for almost half a century to avoid waiting times within processes, to distribute calculations more intelligently and on demand, to take into account the heterogeneity of resources, delais, etc These modern approaches to distributing calculations in a collection of computation units often prove, in practice, to be able to solve a problem faster than more traditional approaches; but in theory, evidence of convergence (and speed of convergence) is generally more difficult to obtain. The approach has consisted of tracking down, modeling, and studying theoretically these complex dynamics that occur in biology and computer science, and to take benefits at the application level. A relatively substantial part has been added concerning the various applications of this theoretical work in various disciplines related to computer science and biology This new part makes this article a complete one, containing the various interesting aspects related to asynchronous iterations. This article will conclude with a discussion, in which the applications of such an approach to disorder will be discussed, and avenues for theoretical exploration will be proposed
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