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.

@article{paperbot3399,
  title = {The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete)},
  author = {Laure Daviaud and David Purser and Marie Tcheng},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 21, Issue 3},
  year = {2025},
  doi = {10.46298/lmcs-21(3:3)2025}
}