The complexity of additive computations of the sets of integer linear forms

An additive computation of a set of linear forms may be presented as the consequence of square matrices $Q_1,\dots,Q_T$ ($Q_i$ equals the unit matrix increased or decreased by 1 in some entry). Thus the additive complexity of a set is the length of the corresponding shortest consequence. A connection between the additive complexity of a set with coefficient matrix $A$ and the complexity of a set with matrix $A^T$ is proved.