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arXiv · 1903.00153

Relational Differential Dynamic Logic

Juraj Kolčák·Ichiro Hasuo·Jérémy Dubut·Shin-ya Katsumata·David Sprunger·Akihisa Yamada
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Abstract

In the field of quality assurance of hybrid systems (that combine continuous physical dynamics and discrete digital control), Platzer's differential dynamic logic (dL) is widely recognized as a deductive verification method with solid mathematical foundations and sophisticated tool support. Motivated by benchmarks provided by our industry partner, we study a relational extension of dL, aiming to formally prove statements such as "an earlier deployment of the emergency brake decreases the collision speed." A main technical challenge here is to relate two states of two dynamics at different time points. Our main contribution is a theory of suitable simulations (a relational extension of differential invariants that are central proof methods in dL), and a derived technique of time stretching. The latter features particularly high applicability, since the user does not have to synthesize a simulation out of the air. We derive new inference rules for dL from these notions, and demonstrate their use over a couple of automotive case studies.

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Juraj Kolčák, Ichiro Hasuo, Jérémy Dubut, Shin-ya Katsumata, David Sprunger, Akihisa Yamada. 2019-03-01. Relational Differential Dynamic Logic. https://arxiv.org/abs/1903.00153

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