Facetal abstraction for non-linear dynamical systems based on δ-decidable SMT.

Formal analysis of non-linear continuous and hybrid systems is a hot topic. A common approach builds on computing a suitable finite discrete abstraction of the continuous system. In this paper, we propose a facetal abstraction which eliminates certain drawbacks of existing abstractions. The states of our abstraction are built primarily from facets of a polytopal partitioning of the system's state space taking thus into account the flow of the continuous dynamics and leading to global over-approximation. The transition system construction is based on queries solved by a δ-decision SMT-solver. The method is evaluated on several case studies.