Question: Exercise 7.28 (Elementary Bi-Decomposition of the Incompletely Specified Function g2q(x), g2r(x)). Check for each pair of variables whether for the incompletely specified function with the

Exercise 7.28 (Elementary Bi-Decomposition of the Incompletely Specified Function g2q(x), g2r(x)). Check for each pair of variables whether for the incompletely specified function with the mark function g2q(x) and g2r(x) calculated in Task 6 of Exercise 7.27 a bi-decomposition with regard to the OR-, AND- and EXOR-operation exists. Practical tasks:

1 Load the TVL system e73dec3.sdt of Exercise 7.27. This TVL system includes the function g2q(x) as object number 30 and g2r(x) as object number 31.

2 Prepare a PRP that checks for each pair of the 4 variables based on

(7.112), (7.113), and (7.114) in [18] whether an EXOR-bi-decomposition of the incompletely specified function exists.

3 Are there any strong OR-bi-decompositions? Use the PRP of Task 2 of Exercise 7.26.

4 Are there any strong AND-bi-decompositions? Use the PRP of Task 3 of Exercise 7.26.

5 Are there any strong EXOR-bi-decompositions?

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