2 research outputs found
The simplified weighted sum function and its average sensitivity
In this paper we simplify the definition of the weighted sum Boolean function
which used to be inconvenient to compute and use. We show that the new function
has essentially the same properties as the previous one. In particular, the
bound on the average sensitivity of the weighted sum Boolean function remains
unchanged after the simplification.Comment: 9 page
The Minimal and Maximal Sensitivity of the Simplified Weighted Sum Function
Sensitivity is an important complexity measure of Boolean functions. In this
paper we present properties of the minimal and maximal sensitivity of the
simplified weighted sum function. A simple close formula of the minimal
sensitivity of the simplified weighted sum function is obtained. A phenomenon
is exhibited that the minimal sensitivity of the weighted sum function is
indeed an indicator of large primes, that is, for large prime number p, the
minimal sensitivity of the weighted sum function is always equal to one.Comment: 6 page