Weak quantifier elimination for the full linear theory of the integers

@article{Lasaruk2007WeakQE,
  title={Weak quantifier elimination for the full linear theory of the integers},
  author={Aless Lasaruk and Thomas Sturm},
  journal={Applicable Algebra in Engineering, Communication and Computing},
  year={2007},
  volume={18},
  pages={545-574}
}
We describe a weak quantifier elimination procedure for the full linear theory of the integers. This theory is a generalization of Presburger arithmetic, where the coefficients are arbitrary polynomials in non-quantified variables. The notion of weak quantifier elimination refers to the fact that the result possibly contains bounded quantifiers. For fixed choices of parameters these bounded quantifiers can be expanded into disjunctions or conjunctions. We furthermore give a corresponding… CONTINUE READING