Attribute Estimation and Testing Quasi-Symmetry

A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every quasi-symmetric function and, except with an error probability at most δ > 0, rejects every function that differs from every quasi-symmetric function on at least a fraction ε > 0 of the inputs. For a function of n arguments, the test probes the function at O (