Asymptotically optimal in unreliability circuits in the basis consisting of the Webb function in P₃ under faults of type 2 at the outputs of elements | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2020. № 47. DOI: 10.17223/20710410/47/3

We consider the realization of ternary logic functions by circuits from unreliable elements in full basis consisting of the Webb function. We assume that elements of the circuit pass to fault states independently of each other, and they are exposed to singletype constant faults of type 2 at the outputs. It is proved that any function of ternary logic can be realized by an asymptotically optimal in reliability circuit functioning with unreliability which is asymptotically no more 3varepsilon with ε → 0. A class of functions is found (it contains almost all ternary logic functions), each of which cannot be implemented by a circuit whose unreliability is asymptotically less 3ε with ε → 0. Thus, it is proved that almost any function of ternary logic can be implemented by an asymptotically optimal on reliability circuit operating with unreliability which is asymptotically equal to 3ε with ε → 0.