Highlights We show how deep learning can be applied for COVID-19 detection from chest X-rays; The proposed method is aimed to mark as first step a chest X-ray as related to a healthy patient or to a patient with pulmonary diseases, the second step is aimed to discriminate between generic pulmonary disease and COVID-19. The last step is aimed to detect the interesting area in the chest X-ray (to provide explainability); We propose an explainable method aimed to automatically detect the areas of interest in the chest X-ray, symptomatic of the COVID-19 disease. We obtain an accuracy of 0.99 in COVID-19 detection by evaluating 6,113 chest x-rays, with a time window required for the detection approximately equal to 2.5 seconds.

In model checking for temporal logic, the correctness of a system with respect to a desired behavior is verified by checking whether a structure that models the system satisfies a formula describing the behavior. Most existing verification techniques are based on a representation of the system by means of a labeled transition system. In this approach to verification, the efficiency of the model checking is essentially influenced by the number of states of the transition system. In this paper we present a new temporal logic, the selective mu-calculus, and an equivalence between transition systems based on the formulae of this logic. This property preserving equivalence can be used to reduce the size of transition systems. The equivalence (called \-equivalence) is based on the set, \, of actions occurring inside the modal operators of a selective mu-calculus formula. We prove that the \-equivalence coincides with the equivalence induced by the set of the selective mu-calculus formulae with occurring actions in \. Thus, a formula can be more efficiently checked on a transition system \-equivalent to the standard one, but smaller than it, since all the actions not in \ are``discarded.'' 1999 Academic Press

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