Platzer, Andre - A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

lmcs:720 - Logical Methods in Computer Science, November 26, 2012, Volume 8, Issue 4
A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

Authors: Platzer, Andre

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.


Source : oai:arXiv.org:1206.3357
DOI : 10.2168/LMCS-8(4:17)2012
Volume: Volume 8, Issue 4
Published on: November 26, 2012
Submitted on: June 25, 2015
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,Mathematics - Dynamical Systems,F.3.1, F.4.1, D.2.4, C.1.m, C.2.4, D.4.7


Share

Browsing statistics

This page has been seen 24 times.
This article's PDF has been downloaded 10 times.