Recall that the negative Davio decomposition expresses a boolean function \( f(x, y, z) \) as \( f(x, y, z) = \overline{z} \cdot f(x, y, 0) + z \cdot f(x, y, 1) \). How can this be adapted to decompose \( f \) into \( z + h(x, y) \)?

For the decomposition \( f(x, y, z) = z + h(x, y) \), derive the conditions under which this holds true by analyzing the truth table of \( f \). What must be true about \( f(x, y, 0) \) and \( f(x, y, 1) \) for this decomposition to be valid?

Generalize the decomposition \( f(x, y, z) = z + h(x, y) \) to account for cases where \( f \) cannot be directly expressed in this form. What additional term or transformation is required to handle such cases, and how does it relate to the negative Davio decomposition?