Exercise 7.34 (Complete Bi-Decomposition of h6(x)). Check first for each pair of variables whether a bi-decomposition exists with regard to the OR-, AND- and EXOR-operation for the function h6(x). Extend the found elementary bi-decompositions to complete bi-decompositions. Select the best existing bi-decomposition and calculate the decomposition functions.

Practical tasks:

1 Load the TVL system e73dec8.sdt of Exercise 7.33. This TVL system includes the function h6(x) as object number 21.

2 Prepare a PRP that checks for each pair of the three variables based on (7.86) in [18] whether an OR-bi-decomposition exists.
3 Prepare a PRP that checks for each pair of the three variables based on (7.90) in [18] whether an AND-bi-decomposition exists.
4 Prepare a PRP that checks for each pair of the three variables based on (7.93) in [18] whether an EXOR-bi-decomposition exists.
5 Are there strong one-to-one OR-bi-decompositions?
6 Are there strong one-to-one AND-bi-decompositions?
7 Are there strong one-to-one EXOR-bi-decompositions?
8 Are there strong one-to-two bi-decompositions?
9 Calculate the function g7 of the existing AND-bi-decomposition with regard to (x2, x3) based on (7.91) in [18] as object 22. Show the Karnaughmap of the calculated function g7(x2, x4).
10 Calculate the function h7 of the existing AND-bi-decomposition with regard to (x2, x3) based on (7.92) in [18] as object 23. Show the Karnaughmap of the calculated function h7(x3, x4).
11 Verify the calculated decomposition.
12 Remove the intermediate TVL and store for later use the TVL system as e73dec9.sdt.