Computing Quadratic Invariants with Min- and Max-Policy Iterations: A Practical Comparison

Policy iterations have been known in static analysis since a small decade. Despite the impressive results they provide – achieving a precise fixpoint without the need of widening/narrowing mechanisms of abstract interpretation – their use is not yet widespread. Furthermore, there are basically two dual approaches: min-policies and max-policies, but they have not yet been practically compared. Multiple issues could explain their relative low adoption in the research communities: implementation of the theory is not obvious; initialization is rarely addressed; integration with other abstraction or fixpoint engine not mentionned; etc. This paper tries to present a Policy Iteration Primer, summarizing the approaches from the practical side, focusing on their implementation and use. We implemented both of them for a specific setting: the computation of quadratic templates, which appear useful to analyze controllers such as found in civil aircrafts or UAVs.