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 solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.

翻译：我们针对如下问题给出了完整的复杂度分类：给定一个固定的有限幺半群上的方程组，在已知该方程组在更受限的幺半群上存在解的情况下，寻找其解。作为推论，我们得到了群上同一问题的复杂度分类。