Bridging Discrete and Continuous Time Models with Atoms

Recent trends in replacing traditionally digital components with analog counterparts in order to overcome physical limitations have led to an increasing need for rigorous modeling and simulation of hybrid systems. Combining the two domains under the same set of semantics is not straightforward and often leads to chaotic and non-deterministic behavior due to the lack of a common understanding of aspects concerning time. We propose an algebra of primitive interactions between continuous and discrete aspects of systems which enables their description within two orthogonal layers of computation. We show its benefits from the perspective of modeling and simulation, through the example of an RC oscillator modeled in a formal framework implementing this algebra.