FDD QUESTION

Question

for Belowquestions i got below answers:

a) (a&b&c) xor (b&c) xor (a&c) xor c xor (a&b) xor b  xor true

b){{a,b,c};{b,c};{a,c};{c};{a,b};{b};{}}

what is wrong with my solution.

how we can check my solutions is wrong or right in teaching?

Can some one help me out. 

Comments

It seems that your FDD (a)), and your ZDD (b)) have the same set representation. Most of the time, this isn't the case.

A fellow student had a similar question, maybe you can learn from the answers we gave: https://q2a.cs.uni-kl.de/584/exercise-sheet-3-question-3-b

As Amala pointed our, your RMNF has a little bug. To me, it looks like you made a slight mistake at the a-node. You seem to have annotated the a-node with {{a},{}}. It should just be {{a}}. Why? The 0-leaf is annotated with {} (empty set), the 1-leaf is annotated with {{}} (set containing the empty set). At the a-node (and every other node as well), we just copy the contents of the low-child-set, and add our variable name (here “a”) to each element of the high-child-set. The low-child-set is {}, the empty set from the 0-leaf. It has no element, so nothing to copy from. The high-child-set is {{}}, the set containing the empty set from the 1-leaf. It's only element is the empty set. To this one, we add a. Thus, we have {{a}}, a set containing nothing but a set containing only a.

---

One more thing (a bit off-topic): Your quite tiny screenshot has been pasted in a rather huge canvas. This leaves quite much whitspace to scroll over. Modern browsers like Firefox have a built-in screenshot-feature (right click → screenshot) that can select particular parts of a website and directly save them as a file.

Answer 1

The solution for the set representation of the FDD is only partially correct. It seems you made some mistake in one of the steps.

1. Leaf node 1 is assigned an set of empty set {{}} and leaf node 0 is assigned an empty set {}.

2. Then as we proceed to the next level and we create set by combining the sets from its low and high branch. We add the literal to sets in the high branch of that node. For low branch we just copy the set from the low branch. Then we combine it to form a set of sets of that node. 

3. Once you get the set representation of the FDD, then you can compute the RMNF from it.