Towards formal verification of analog designs

We show how model checking methods developed for hybrid dynamic systems may be usefully applied for analog circuit verification. Finite-state abstractions of the continuous analog behavior are automatically constructed using polyhedral outer approximations to the flows of the underlying continuous differential and difference equations. In contrast to previous approaches, we do not discretize the entire continuous state space, and our abstraction captures the relevant behaviors for verification in terms of the transitions between "states" (regions of the continuous state space) as a finite state machine in the hybrid system model. The approach is illustrated for two circuits, a standard oscillator benchmark, and a much larger and more realistic delta-sigma (AI) modulator.