We show how the language of Krivine's classical realizability may be used to specify various forms of nondeterminism and relate them with properties of realizability models. More specifically, we introduce an abstract notion of multi-evaluation relation which allows us to finely describe various nondeterministic behaviours. This defines a hierarchy of computational models, ordered by their degree of nondeterminism, similar to Sazonov's degrees of parallelism. What we show is a duality between the structure of the characteristic Boolean algebra of a realizability model and the degree of nondeterminism in its underlying computational model. ACM Reference Format:Guillaume Geoffroy. 2018. Classical realizability as a classifier for nondeterminism.

We develop a technique for representing and preserving cardinals in realizability models, and we apply this technique to define a realizability model of Zorn’s lemma restricted to an ordinal.

Drowsiness detection is still an open issue, especially when detection is based on physiological signals. In this sense, light non-invasive modalities such as electroencephalography (EEG) are usually considered. EEG data provides informations about the physiological brain state, directly linked to the drowsy state. Electrocardigrams (ECG) signals can also be considered to involve informations related to the heart state. In this study, we propose a method for drowsiness detection using joint EEG and ECG data. The proposed method is based on a deep learning architecture involving convolutional neural networks (CNN) and recurrent neural networks (RNN). High efficiency level is obtained with accuracy scores up to 97% on validation set. We also demonstrate that a modification of the proposed architecture by adding autoencoders helps to compensate the performance drop when analysing subjects whose data is not presented during the learning step.