Synchronous orders on the set of integers
Formal Languages and Automata Theory
2023-10-06 v2
Abstract
A binary relation over a free monoid is synchronous if it can be recognized by a synchronous automaton that reads its two tapes simultaneously. We consider the case where the free monoid is generated by a single element (which makes it isomorphic to the additive monoid of integers) and where the binary relation recognized is a strict order. Our main results are: given such an automaton it is possible to determine whether or not is has infinite chains or antichains; we characterize the orders that are linear; given two linear synchronous orders we show how to determine whether or not they are equivalent.
Keywords
Cite
@article{arxiv.2309.09566,
title = {Synchronous orders on the set of integers},
author = {Christian Choffrut},
journal= {arXiv preprint arXiv:2309.09566},
year = {2023}
}