On the Expressiveness of Büchi Arithmetic
Christoph Haase, Jakub Różycki · Lecture notes in computer science · 2021
Abstract 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 $$\varSigma _2$$ 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.