VC-Dimensions of Short Presburger Formulas


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.

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Correspondence to Danny Nguyen.

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Nguyen, D., Pak, I. VC-Dimensions of Short Presburger Formulas. Combinatorica 39, 923–932 (2019).

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Mathematics Subject Classification (2010)

  • 03C45
  • 52C07