Determination of the correct criteria for K-systems reconstruction

Abstract

One of the essential components of the K-system reconstruction process is the determination of which state or substate contributes the greatest to the reconstruction. In the literature, there have been two competing criteria used, both of which are based upon a quantity known as the ‘information-theoretic transmission’, which is defined as , where k is the information in the actual substate, and k′ is the information in the reconstructed substate. One approach uses this quantity, while the other uses the quantity . It had been implicitly assumed that both approaches gave the same result (i.e. the substate that would make the greatest contribution to the reconstruction would have a maximum value for both of these quantities). In this paper, we show empirically that in general they do not give the same results, and that the latter criterion predicts the substate that yields the optimal reconstruction. We then derive the correct criterion and demonstrate that this result is consistent with fundamental principles of information theory.

Keywords:

• K-systems analysis
• reconstructability analysis
• information theoretic transmission
• substates
• system function