We study the problem of counting the repairs of an inconsistent database in the case where constraints are Functional Dependencies (FDs). A repair is then a maximal independent set of the conflict graph, wherein nodes represent facts and edges represent violations. We establish a dichotomy in data complexity for the complete space of FDs: when the FD set has, up to equivalence, what we call a “left-hand-side chain,” the repairs can be counted in polynomial time; otherwise, the problem is $♯\mathbf{P}$-complete. Moreover, the property of having a left-hand-side chain up to equivalence coincides with the condition that the conflict graph of every inconsistent database for the schema is $P_4$-free, and it is polynomial-time decidable.

我们研究了在约束为功能依赖关系（FD）的情况下计算不一致数据库的修复次数的问题。因此，修复是冲突图的最大独立集合，其中节点代表事实，边缘代表违规。我们为FD的整个空间建立了数据复杂度的二分法：当FD集具有等价的所谓的“左手链”时，修复次数可以用多项式计算；否则，问题是$♯\mathbf{P}$-完成。此外，具有等价的左侧链的属性与以下条件一致：该模式的每个不一致数据库的冲突图为$P_4$-free，并且可以确定多项式时间。