  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.
