On the Expressiveness of Büchi Arithmetic

10/24/2020

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by   Christoph Haase, et al.

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We show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its Σ_2-fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of Büchi arithmetic.