Quantified Differential Dynamic Logic for Distributed Hybrid Systems

  • André Platzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6247)

Abstract

We address a fundamental mismatch between the combinations of dynamics that occur in complex physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic networks, where neither structure nor dimension stay the same while the system follows mixed discrete and continuous dynamics.

We provide the logical foundations for closing this analytic gap. We develop a system model for distributed hybrid systems that 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 it. We prove that this 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 new cars may appear dynamically on the road.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • André Platzer
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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