Minimal universal elements in the class of neural circuits

A. A. Chasovskikh^a, M. V. Agafonova^a, A. A. Khusaenov^a, E. I. Yakovenko<sup>b

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Lomonosov Moscow State University

Abstract: In the class of circuits constructed from linear elements over the ring of binary-rational numbers and the Heaviside function, all universal circuits of minimal complexity have been found.

Keywords: binary rational numbers, linear function, Heaviside function, neural circuit, superposition operations, circuit complexity, completeness, universal element.

UDC: 519.716.3

Received: 20.08.2025

DOI: 10.4213/dm1893