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[ + ].
This work was partially supported by CRUI/DAAD under the project “Programma Vigoni: Reducing complexity by introducing structure”, by the European Science Foundation (ESF) for the activity entitled “Automata: from Mathematics to Applications”, and by the Italian MURST under the project “PRIN: Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali: metodi probabilistici e combinatori in ambito di linguaggi formali”.
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Choffrut, C., Malcher, A., Mereghetti, C., Palano, B. (2010). On the Expressive Power of FO[ + ]. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_16
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DOI: https://doi.org/10.1007/978-3-642-13089-2_16
Publisher Name: Springer, Berlin, Heidelberg
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