On the Expressive Power of FO[ + ]
The characterization of the class of FO[ + ]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study some closure properties of FO[ + ]-definable languages which, as a by-product, allow us to give an alternative proof that the Dyck languages cannot be defined in FO[ + ].
KeywordsBounded languages semilinear sets first order logic
Unable to display preview. Download preview PDF.