Hard Problem to solve with GP

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Hard Problem to solve with GP

Bernardo Pereira Nunes
Hi All,

I am trying to solve a problem using GP. However I am a little bit
confused. Someone can help me?

The problem is:

I have two sets S1:{a,b,c} and S2:{f,g} and then I want to verify if
these two sets share some equivalence.

Imagine that (a Union b) is equivalent to the set f from S2. So, I would
like to have as a solution the followinf result: (a U b) ~ f

In the same way, I can say that c and g are equals, so the result will
be given by the individuum: c ~ g

I cant imagine in a solution to this problem. I can imagine that if I
determine one set from S1 then I can run the GP and get a solution.
However I want to verify all possibilities in the same time. I mean, in
the left side I try some combination and then in the right side another
combination. Im looking for equivalences between the two sets.

My first question is: How to create the operator "~" where the variables
of the set S1 will be in the left side of the operator "~" and the
variables of the se S2 will be in the right side. How to determine this
operator as a root, and then how to determine the left variables and the
right variables for this problem.

Second Question: How to define a variable to appear just once. I mean, a
U b and not a U a U a U b.

Please send me suggestions.

Thank you in advance!


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