Exercise 7.26 (Strong Elementary Bi-Decomposition of the Completely Specified Function g1(x)). Check for each pair of variables whether for the function g1(x) of Fig. 7.10

a) on page 182 exists a bi-decomposition with regard to the OR-, AND- and EXOR-operation. Practical tasks:

1 Load the TVL system e73dec2.sdt of Exercise 7.25. This TVL system includes the function g1(x) as object number 10. Copy for universal use in the PRPs the function g1(x) as object number 30 and create their complement as object number 31.

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

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

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

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

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

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

5 Are there any strong OR-bi-decompositions?

6 Are there any strong AND-bi-decompositions?

7 Are there any strong EXOR-bi-decompositions?