Recently, while working on a research project, I got on a tangent. From this tangent, I got on another tangent and that is what I want to write about today: **a very nice Boolean function**. This example got rediscovered several times for different reasons and, as I try to emphasize from time, I believe that things that are getting rediscovered many times must be of particular importance.

So let us define our Boolean function. I will give three very similar definitions throughout this post, but I will start with only one. Put . Our Boolean function is defined as follows: Put (as ). For , write as with and . Then use this rule:

- If , then .
- If , then .
- If , then .
- If , then .

In the following, we list some properties of this function. Many of the concepts here are also discussed in an earlier post of mine.