On the complexity of implementation of a system of three monomials of two variables by composition circuits

We study the complexity of implementation of systems of monomials by composition circuits. Here, by the complexity we mean the smallest possible number of operations required for computation of the system of monomials from the variables; under this approach, results of intermediate computations can be used several times. The main result of this paper establishes, for an arbitrary system of three monomials of two variables without zeroth powers, a formula for the complexity of their joint implementation by composition circuits with an additive error which is either 1 or 0.