Definability by deterministic and non-deterministic programs (with applications to first-order dynamic logic)

We make explicit a connection between the “unwind property” and first-order logics of programs. Using known results on the unwind property, we can then quickly compare various logics of programs. In Section 1, we give a sample of these comparative results, which are already known but established differently in this paper. In Sections 2 and 3, given an arbitrary deterministic regular program S (with or without parameterless recursive calls), we show how to construct a first-order structure where S will unwind. Based on this construction, we then prove that the logic of regular programs (with or without parameterless recursive calls) is more expressive than the logic of deterministic regular programs (with or without parameterless recursive calls, respectively).