Each of the summation terms differs from the original expression for G(λ 1 , λ 2 ) in exactly one multiplier whose partial derivative with respect to λ 1 is computed.
in order to construct a functional automaton for ∂F ∂λ 1 we can take two disjoint copies of the original functional automaton, see Figure 3, and set transitions between them in order to reflect the partial derivatives with respect to λ 1 of the single multipliers.