International Encyclopedia of Systems and Cybernetics

A. RAMER and L. LANDER describe the following problems, met in reconstructability analysis:

"Approximation problem

If the reconstructed system is different from the original one (and… this is almost invariably the case). how close can we come to that original system?

"Complexity problem

Exhaustive search through the spaces of possible reconstructions exhibit hyper-exponential complexity and therefore are numerically intractable. There is therefore a need for heuristics that may guide the search and thus limit its complexity. The questions dealing with existence, characterization and applicability of methods that may obviate the necessity of a complete search can be described as the complexity issue

"Consistency problem (Local)

Structure systems encountered in practice often exhibit a lack of consistency in that the marginal distributions, derived from the various parts of the system, do not quite agree. This inconsistency is called local, and we would often like to consider it as a minor one. Can it somehow be tolerated and can we still arrive at a reasonable reconstruction?

"Consistency problem (Global)

Given an arbitrary, locally consistent family of systems, can we determine whether they admit a reconstruction and are thus globally consistent?

"Labeling problem

Can a family of simple variables be selected to form a system of distinct representatives for the elements of a given structure system? Here we have actually two distinct problems. One is the very question of existence of such a system of representatives, and the other concerns the usefulness and meaning of such a selection… In reconstructability theory we view them as the labeling systems for the general structure

"Proximity problem

What numerical measures are suitable for determining the proximity of two reconstructions? Is anyone such measure superior to another? Can such measures be considered metrics or norms on appropriate space of recon struction?

"Reconstruction family problem

The determination of all admissible overall systems which agree with a given structure system

"Recovery problem

Given a structure system, which originated from an overall system, how can that system be rebuilt, or even an overall system that would agree with our structure system?

"Solution problem

Given only a consistent family of systems (thus a structure system), how can we identify, among all the candidate reconstructions, the optimal one?" (1990, p.449-50)

This all sounds quite esoteric. A case example could be very useful.