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 formula

Authors: Christian Choffrut ; Achille Frigeri

    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.


    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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