On the expressive power of FO[+]

Authors:
Christian Choffrut;Andreas Malcher;Carlo Mereghetti;Beatrice Palano
Affiliations:
LIAFA, UMR 7089, Paris 13, France;Institut für Informatik, Universität Giessen, Giessen, Germany;DSI, Università degli Studi di Milano, Milano, Italy;DSI, Università degli Studi di Milano, Milano, Italy
Venue:
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Year:
2010

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Abstract

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[+].