English

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}
}