VC-Dimensions of Short Presburger Formulas

  • Danny NguyenEmail author
  • Igor Pak


We study VC-dimensions of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the formula.

Mathematics Subject Classification (2010)

03C45 52C07 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsUCLALos AngelesUSA

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