The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete)
Formal Languages and Automata Theory
2025-07-16 v4 Logic in Computer Science
Abstract
We show that the big-O problem for max-plus automata is decidable and PSPACE-complete. The big-O (or affine domination) problem asks whether, given two max-plus automata computing functions f and g, there exists a constant c such that f < cg+ c. This is a relaxation of the containment problem asking whether f < g, which is undecidable. Our decidability result uses Simon's forest factorisation theorem, and relies on detecting specific elements, that we call witnesses, in a finite semigroup closed under two special operations: stabilisation and flattening.
Keywords
Cite
@article{arxiv.2304.05229,
title = {The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete)},
author = {Laure Daviaud and David Purser and Marie Tcheng},
journal= {arXiv preprint arXiv:2304.05229},
year = {2025}
}