Christian Choffrut ; Achille Frigeri - Deciding whether the ordering is necessary in a Presburger formula

dmtcs:510 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 1 - https://doi.org/10.46298/dmtcs.510
Deciding whether the ordering is necessary in a Presburger formulaArticle

Authors: Christian Choffrut 1; Achille Frigeri 1,2

  • 1 Laboratoire d'informatique Algorithmique : Fondements et Applications
  • 2 Dipartimento di Matematica, "Francesco Brioschi"

We characterize the relations which are first-order definable in the model of the group of integers with the constant 1. This allows us to show that given a relation defined by a first-order formula in this model enriched with the usual ordering, it is recursively decidable whether or not it is first-order definable without the ordering.

https://doi.org/10.46298/dmtcs.510
Source: HAL:hal-00990437v1
Volume: Vol. 12 no. 1
Section: Automata, Logic and Semantics
Published on: January 1, 2010
Imported on: March 26, 2015
Keywords: Presburger arithmetics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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