We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. The first is an $O(\log n)$-approximation algorithm, based on the submodular goal-value approach of Deshpande, Hellerstein and Kletenik. Our second algorithm, which is simple, is based on the algorithm solving the SBFE problem for $k$-of-$n$ functions, due to Salloum, Breuer, and Ben-Dov. It achieves a $(B-1)$ approximation factor, where $B$ is the number of blocks of 0's and 1's in the standard vector representation of the symmetric Boolean function. As part of the design of the first algorithm, we prove that the goal value of any symmetric Boolean function is less than $n(n+1)/2$. Finally, we give an example showing that for symmetric Boolean functions, minimum expected verification cost and minimum expected evaluation cost are not necessarily equal. This contrasts with a previous result, given by Das, Jafarpour, Orlitsky, Pan and Suresh, which showed that equality holds in the unit-cost case.

翻译：我们给出了两种近似算法来解决对称布尔函数的 Stochastec Boulean 函数评估问题。 首先是基于 Deshpande、 Hellerstein 和 Kletenik 的子模块目标值方法的O( log n) 和 occol 算法。 我们的第二个算法很简单, 其基础是解决SBFE 问题的方法, 其原因是Salloum、 Breuer 和 Ben- Dov 。 它达到一个$( B-1 ) 的近似系数, 其中, $B$ 是 Boolean 函数标准矢量中0 和 1 的区块数。 作为第一个算法设计的一部分, 我们证明任何对称布林函数的目标值低于 $( n+1 / 2 美元 ) 。 最后, 我们举一个例子, 表明对称 Boolean 函数, 最小的预期核查成本和最小的预期评价成本不一定相等 。 这个比对 Panlifar 和 Parfar 来说, 这个单位的对比是 。