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.

翻译：我们证明最大加自动机的Big-O问题是可判定的且是PSPACE-完备的。Big-O（或仿射支配）问题询问：给定两个计算函数f和g的最大加自动机，是否存在常数c使得f < cg + c。这是包含问题（询问是否f < g，该问题不可判定）的一种松弛形式。我们的可判定性结果使用了西蒙森林因式分解定理，并依赖于在一个有限半群中检测特定元素（我们称之为见证者），该半群在两种特殊运算下封闭：稳定化和扁平化。