Exercise 7.24 (Strong Elementary Bi-Decomposition of the Completely Specified Function y = f(x)). Check for each pair of variables whether a bi-decomposition with regard to the OR-, AND- and EXOR-operation exists for the function of Fig. 7.1. Practical tasks:

1 Load the final TVL system of Exercise 7.9. This TVL system includes the list of phases F(x, y) as object number 4. Calculate the function f(x). Store this TVL system as e73dec1.sdt for later use.

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

(7.86) in [18] whether an OR-bi-decomposition exists.

3 Prepare a PRP that checks for each pair of the six variables based on

(7.90) in [18] whether an AND-bi-decomposition exists.

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

(7.93) in [18] whether an EXOR-bi-decomposition exists.

5 Are there any OR-bi-decompositions?

6 Are there any AND-bi-decompositions?

7 Are there any EXOR-bi-decompositions?