 Firstly, decomposition of a function into non-interacting components generally permits more economical representations of the function.For example, on a set of quaternary (i.e., 4-ary) variables, representing the full function formula_22 requires storing formula_23 values, the value of the function for each element in the Cartesian product formula_24, i.e., each of the 1024 possible combinations for formula_24.However, if the decomposition into formula_12 given above is possible, then formula_27 requires storing 4 values, formula_28 requires storing formula_29 values, and formula_30 again requires storing just 4 values.