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 -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}
}