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Abstract. In this paper, we consider the computational power of a new variant of networks of evolutionary processors which seems to be more suitable for a software and hardware implementation. Each processor as well as the data navigating throughout the network are now considered to be polarized. While the polarization of every processor is predefined, the data polarization is dynamically computed by means of a valuation mapping. Consequently, the protocol of communication is naturally defined by means of this polarization. We show that tag systems can be simulated by these networks with a constant number of nodes, while Turing machines can be simulated, in a time-emcient way, by these networks with a number of nodes depending linearly on the tape alphabet of the Turing machine.

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Due to the growing rise of cyber attacks in the Internet, the demand of accurate intrusion detection systems (IDS) to prevent these vulnerabilities is increasing. To this aim, Machine Learning (ML) components have been proposed as an efficient and effective solution. However, its applicability scope is limited by two important issues: (i) the shortage of network traffic data datasets for attack analysis, and (ii) the data privacy constraints of the data to be used. To overcome these problems, Generative Adversarial Networks (GANs) have been proposed for synthetic flow-based network traffic generation. However, due to the ill-convergence of the GAN training, none of the existing solutions can generate high-quality fully synthetic data that can totally substitute real data in the training of ML components. In contrast, they mix real with synthetic data, which acts only as data augmentation components, leading to privacy breaches as real data is used. In sharp contrast, in this work we propose a novel and deterministic way to measure the quality of the synthetic data produced by a GAN both with respect to the real data and to its performance when used for ML tasks. As a by-product, we present a heuristic that uses these metrics for selecting the best performing generator during GAN training, leading to a novel stopping criterion, which can be applied even when different types of synthetic data are to be used in the same ML task. We demonstrate the adequacy of our proposal by generating synthetic cryptomining attacks and normal traffic flow-based data using an enhanced version of a Wasserstein GAN. The results evidence that the generated synthetic network traffic can completely replace real data when training a ML-based cryptomining detector, obtaining similar performance and avoiding privacy violations, since real data is not used in the training of the ML-based detector.