This is what "grammar-based compression algorithms" do.  You should be
able to find many by searching for those words.

Flo wrote:
> I am searching an algorithm that can find common parts within a set of
> given strings. For example given the four strings
>
> MinXBla MinYBla MinPhiBla MinThetaBla
>
> The algorithm should see that the strings start with Min, then comes a
> variable string, and then they end with Bla. An extra would be if it
> would also return the list of variable strings, here {X,Y,Phi,Theta}.
>
> What if I add another level? For example given the 8 strings:
>
> fMinXBla fMinYBla fMinPhiBla fMinThetaBla
> nMinXBla nMinYBla nMinPhiBla nMinThetaBla
>
> Where we have almost the same situation as before, however a variable
> string is prepended to each string. The list of variables is now 2
> dimensional {f,n}{X,Y,Phi,Theta}.
>
> I am happy if somebody knows the name such an algorithm, if it exists,
> so I can look up the details myself. 
> 
> Greetings
> 
> Flo


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