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When designing new digital instruments and devices, there are a vast variety of reasons why the finally designed devices will malfunction. To decrease the number of such failures and to increase design accuracy, various methods and systems for modeling digital devices are used. In these systems, various methods for describing signals in models of designed devices can be used. In this case, three-valued, four-valued, ..., nine-valued, thirteen-valued, as well as analog signal descriptions can be applied. Increasing signal and element models complexity in digital devices allows designing more accurate models. However, when modeling digital devices, multi-valued alphabets do not allow to increase the accuracy of modeling and research of dynamic processes in devices. This is due to the impossibility of taking into account processes and interference caused by both stray capacitances and inductances between separate components of the devices and conductors connecting them, as well as dynamic processes, caused by external electromagnetic fields affecting the device designed. Describing such processes using continuous or K-valued differential equations improves the accuracy of digital devices modeling. Nevertheless, the problems of automated testing of these devices and the automation of determining their performance remain unsolved. For automated recognition of failures in the designed digital devices, neural networks, in particular, adaptive resonant theory (ART) neural networks, can be applied, since they have an important property, the ability to retrain when additional information about failures occurs. However, neural networks also have an essential drawback: they do not allow getting more than one solution, although with K-valued differential calculus of digital devices, this can occur quite often, which makes it possible to recognize failures that can be attributed simultaneously to two or more different classes of errors, and, therefore, to recognize failures, which can be simultaneously assigned to two or more different classes, and consequently, get more accurate results. In this regard, it is necessary to develop neural networks that could recognize two or more possible solutions (or types of failures). This would expand the field of failures automated detection in the designed digital devices and determine the performance accuracy. Figs.: 3. Refs: 12 titles.