Abstract. We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road. 1.

Network (VANET) technologies provide a unique opportunity to develop various types of communication-based automotive applications. In this chapter, we focus primarily on four major aspects: (a) description of communication-based automotive applications, (b) investigating the application characteristics and network attributes, (c) classifying the applications into categories, and (d) defining market perspectives and deployment challenges for each class of applications. To date, many applications have been identified by the automotive research community. From a value or customer benefit perspective, these applications can be roughly organized into three major classes: safety-oriented, convenience-oriented, and commercial-oriented, and they vary significantly in terms of application characteristics. We begin by describing communication-based automotive applications that span both the Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication modes. We follow a systematic classification methodology for such applications that goes through two major steps: characterization and classification. We focus on a rich subset of representative applications and characterize them with respect to plausible application- and networkingrelated attributes. The characterization process not only strengthens our understanding of the applications but also sets the stage for the classification step, since it reveals numerous