The algebra of binary trees is affine complete
Formal Languages and Automata Theory
2024-02-14 v3
Abstract
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet containing at least three letters, a function is congruence preserving if and only if it is polynomial.
Keywords
Cite
@article{arxiv.2011.03925,
title = {The algebra of binary trees is affine complete},
author = {Andre Arnold and Patrick Cegielski and Serge Grigorieff and Irene Guessarian},
journal= {arXiv preprint arXiv:2011.03925},
year = {2024}
}
Comments
9 pages, 1 figure