We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solut ion over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.

翻译：本文针对在固定有限单调上求解给定方程系统的问题，给出了完整复杂度分类，前提是该方程系统在更受限制的单调上存在解。作为推论，我们得到了群上相同问题的复杂度分类。