Nontrivial definability by flow-chart programs

The ability of flow-chart programs to define relations and functions nondefinable by open first-order formulas is studied. An example of a unary, not locally finite structure Tω (with equality), such that every flow-chart is equivalent in Tω to a loop-free flow-chart, is shown, but the same does not hold for some flow-charts equipped with counters or recursion. From this it is deduced that Deterministic Dynamic Logic of regular programs is strictly weaker than (nondeterminitic) Dynamic Logic. It is also proved that flow-charts with recursion (but without counters) are able to define nontrivial functions in any structure, provided a nontrivial computable function exists over this structure