Restructuring Dynamical Systems for Inductive Verification

Inductive approaches to deductive verification has gained widespread adoption in the control and of safety-critical dynamical systems. The practical success barrier certificates attests their effectiveness ongoing theoretical refinement. However, when conditions are non-inductive, various strategies employed address this issue. One strategy is strengthen property until they arrive at an inductive proof. it not always obvious how one must strengthen a property. Notions strenghtening particularly non-obvious properties interest more expressive than safety or reachability. An alternative technique instead consider xmlns:xlink="http://www.w3.org/1999/xlink">structural changes. These structural changes may either be novel notions induction such as $k$ -induction, encode additional information similar dimension lifting. We posit that reformulating xmlns:xlink="http://www.w3.org/1999/xlink">restructuring system fundamental approaches. This position paper provides overview certificate based connection restructuring. discuss opportunities, challenges, open problems emerging field, paving way for future research framework restructuring holds promise advancing verification, enhancing safety, promoting design insights.