English

On the Expressiveness of B\"uchi Arithmetic

Logic in Computer Science 2021-03-04 v3 Formal Languages and Automata Theory Logic

Abstract

We show that the existential fragment of B\"uchi arithmetic is strictly less expressive than full B\"uchi arithmetic of any base, and moreover establish that its Σ2\Sigma_2-fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of B\"uchi arithmetic.

Cite

@article{arxiv.2010.12892,
  title  = {On the Expressiveness of B\"uchi Arithmetic},
  author = {Christoph Haase and Jakub Różycki},
  journal= {arXiv preprint arXiv:2010.12892},
  year   = {2021}
}
R2 v1 2026-06-23T19:37:00.397Z