In expression (4.29) of f(x) it is not directly visible whether the function is linear with regard to certain variables:

f(x) = x1(x3 ⊕ x2x4) ∨ x1(x2 ⊕ x3)x4 ∨ x1 x3 x4. (4.29)

Check by means of (4.28) whether function (4.29) is linear, separately for each variable of the set {(x1, x2, x3, x4)}. Practical tasks:

1 Write a PRP that detects all linearity properties of the function (4.29)

with regard to each of its variables.

2 Execute this PRP and check for linearity of f(xi, x0) with regard to each of its variables. Use the view of Karnaugh map to check whether a calculated function is equal to 1.

3 If f(xi, x0) is linear with regard to xi then use definition (4.27) in order to calculate the function f(x0) independent on xi.

4 Create the simplified expression of the function and verify it.