Modeling hierarchical combinational circuits

Hierarchical descriptions of combinational circuits often contain apparent loops. Since it may be difficult to distinguish apparent loops from actual loops, it is useful to construct models of combinational circuits that can handle cyclic dependencies. We show that Boolean relations are inadequate for this purpose, and define a ternary model that solves the problem. We use the model to characterize exact solutions to a broad class of substitution and rectification problems. The theory cleanly handles network transformations that might introduce cyclic dependencies.