Neural network to detect connected parameters
That's easy.  Find all configurations where parameter 1 has value A; throw away all the rest.  Now you can easily test whether all the remaining parameters have the same value for parameter 2 (just scan through them and see if they all have the same value as the first); you can do that for parameter 3; and so on.  No fancy algorithm is needed -- it's straightforward to program with a simple linear scan.