We analyse the complexity of approximate counting constraint satisfactions problems $\mathrm{\#}\mathrm{CSP}(\mathcal{F})$, where $\mathcal{F}$ is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is known if $\mathcal{F}$ contains arbitrary unary functions. We strengthen this result by fixing any permissive strictly increasing unary function and any permissive strictly decreasing unary function, and requiring only those to be in $\mathcal{F}$. The resulting classification is employed to characterise the complexity of a wide range of two-spin problems, fully classifying the ferromagnetic case. Furthermore, we also consider what happens if only the pinning functions are assumed to be in $\mathcal{F}$. We show that any set of functions for which pinning is not sufficient to recover the two kinds of permissive unaries must either have a very simple range, or must satisfy a certain monotonicity condition. We exhibit a non-trivial example of a set of functions satisfying the monotonicity condition.

我们分析了近似计数约束满足问题的复杂性 $\mathrm{＃}\mathrm{CSP}（\mathcal{F}）$，在哪里 $\mathcal{F}$是布尔变量的一组非负有理值函数。一个完整的分类是已知的，如果$\mathcal{F}$包含任意一元函数。我们通过修正所有允许的严格增加一元函数和任何允许的严格减少一元函数，并仅要求那些处于$\mathcal{F}$。所得分类用于表征广泛的两自旋问题的复杂性，从而对铁磁情况进行了完全分类。此外，我们还考虑了如果仅假设钉扎功能位于$\mathcal{F}$。我们表明，固定不足以恢复两种允许的一元函数的任何函数集都必须具有非常简单的范围，或者必须满足特定的单调性条件。我们展示了满足单调性条件的一组函数的非平凡示例。