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Complexity of presburger arithmetic with fixed quantifier dimension

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Abstract

It is shown that the decision problem for formulas in Presburger arithmetic with quantifier prefix [∃1∀2 … ∃ m ∀3] (form odd) and [∃1∀2 … ∀ m ∃3] (form even) is complete for the class Σ p m of the polynomial-time hierarchy. Furthermore, the prefix type [∃∀∃∃] is complete for Σ p2 , and the prefix type [∃∀] is complete for NP. This improves results (and solves a problem left open) by Grädel [7].

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  1. Abt. Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany

    U. Schöning

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  1. U. Schöning
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Schöning, U. Complexity of presburger arithmetic with fixed quantifier dimension. Theory of Computing Systems 30, 423–428 (1997). https://doi.org/10.1007/BF02679468

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