Unbounded time verification of hybrid systems is a challenging
problem. In this talk, we discuss how strategy improvement algorithms,
as used for the analysis of two-players zero-sum games, can be applied
for performing template-based unbounded time verification of hybrid
systems using abstract interpretation. In order to do so, we in a
first step recast the verification problem into a purely mathematical
optimization problem. In a second step, we discuss two recently
developed strategy improvement algorithms that can be used to tackle
the obtained mathematical optimization problem. Finally, we discuss
the consequences of using these approaches for performing template-
based unbounded time verification of hybrid systems.