hi,

I’m trying to answer several questions about properties of **randomly uniform generated SDR** with sparsesness of “s”.

Let me know if I’m correct !

First question : given **TWO** SDRs of lengths “n” bits.

- what is the probability that they don’t overlap at all ?
- what is the probability that they match 100% ?
- what is the probability that they overlap by “q” percent of “s” ?

Here is my thinking : the probability that bit at any position is 1 for both vectors is “s*s” i.e. `s^2`

From this it follows that the probability of full match is :` (s^2)^(s*n)`

Then the probability of partial match of q% is of s%*nbits is : `(s^2)^(q*s*n)`

For example if we have : n=100, s=0.02 , q=0.50

the probability of partial match is :

```
-> (0.02^2)^(0.5*0.02*100)
= 0.0004
```

from this it follows that : the probability of no overlap is : 1 - x => 0.9996

m’I correct ?

Next very important question how do I calculate those for “**M**” SDRs, not just TWO ?

Experimentally I’m getting max 8-9bits overlap when : n=2000, sparsity=0.02 and up 5000 random-samples full comparison i.e. 9/40= max 22.5% overlap