A computer-aided circuit design tool can be described as a set of algorithms applied to an internal representation of a circuit design or specification in order to answer specific questions or perform certain operations. The representation directly limits the operations that can be performed as well as the accuracy of the resulting answers. This dissertation concerns the development and exploration of one such design representation and shows how it is appropriate for a wide range of circuit design tasks. Along the way, we discover some new techniques for specification, modeling, simulation, and verification of circuits. We especially consider real-time aspects of circuit behavior, and we present some significant enhancements to existing real-time verification algorithms.