Location-Invariant Properties of Functions Versus Properties of Distributions: United in Testing but Separated in Verification

A property of functions is called location-invariant (or symmetric) if it can be characterized in terms of the frequencies in which each value occurs in the function, regardless of the locations in which each value occurs. It is known that the (query) complexity of testing location-invariant properties of functions is closely related to the (sample) complexity of testing the (corresponding properties of the) corresponding distributions. The main message of the current work is that this close rel...