Deterministic Context-Free Dynamic Logic is More Expressive than Deterministic Dynamic Logic of Regular Programs

We show an example of an algebra T, such that every deterministic regular /flow-chart/ program is equivalent in T to a loop-free approximation of itself, while a program augmented by one binary push-down store is not equivalent in T to any loop-free program. From this we deduce that the Deterministic Dynamic Logic of regular programs is strictly weaker than the Deterministic Context-Free Dynamic Logic.