Unfaithful Glitch Propagation in Existing Binary Circuit Models

We show that no existing continuous-time, binary value-domain model for digital circuits is able to correctly capture glitch propagation. Prominent examples of such models are based on pure delay (P) channels, inertial delay (I) channels, or the elaborate PID channels proposed by Bellido-Díaz et al. We accomplish our goal by considering the solvability/non-solvability border of a simple problem called Short-Pulse Filtration (SPF), which is closely related to arbitration and synchronization. On one hand, we prove that SPF is solvable in bounded time in any such model that provides channels with non-constant delay, like I and PID. However, this is in opposition to the impossibility of solving bounded SPF in real (Newtonian) circuit models, which follows from well-known results on the behavior of bi-stable circuits obtained by Marino. On the other hand, for binary circuit models with pure delay channels, we prove that SPF cannot be solved even in unbounded time. This, however, is in opposition to the fact that one can easily solve the unbounded SPF problem in Newtonian circuit models. Consequently, indeed none of the binary value-domain models proposed so far faithfully captures glitch propagation of real circuits.