On the Expressive Power of FO[ + ]

  • Christian Choffrut
  • Andreas Malcher
  • Carlo Mereghetti
  • Beatrice Palano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)


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[ + ].


Bounded languages semilinear sets first order logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christian Choffrut
    • 1
  • Andreas Malcher
    • 2
  • Carlo Mereghetti
    • 3
  • Beatrice Palano
    • 3
  1. 1.LIAFAUMR 7089Paris 13France
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany
  3. 3.DSIUniversità degli Studi di MilanoMilanoItaly

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