sheet 3:pblm 2

Question

For ZDD i am trying to calculate RMNF i am getting error after doing 4 steps:

Answer 1

As far as I can see, the computation of the set representation of the ZDD is correct, but I guess that you have made typos in that you used ":" instead of "," or ";" to separate the sets. The set representation should be {{a,b},{a,c},{c},{}} and the formula is then 

a & !b & c | a & b & !c | !a & !b & c | !a & !b & !c 

Its RMNF is (you have a mistake there)

a ⊕ a&c ⊕ b ⊕ true

Comments

The RMNF is taken from the set representation as if it was the set representation of an FDD. Actually, the said formula should have been converted to RMNF using (for example) Davio, or by multiplying out a big xor of Min-terms. See also: https://q2a.cs.uni-kl.de/602/exercise-constructing-using-positive-davio-decomposition

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I read the question above in that for a given ZDD, a set representation is to be found, and then a RMNF should be derived for the represented formula. If b means that we should interpret the decision diagram as a FDD, then we do no longer speak about the same formula Phi, right?

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Exactly! The student had just written diagram's set representation as n RMNF. That would only work if it was an FDD. Since it is a ZDD, we have to take the formula from a), and convert it to RMNF using Davio (or the min-term-XOR-trick).