Elasticity conditions for storage versus error exchange in question--Answering systems

It has been conjectured that error-allowance could improve dramatically the performance of data processing systems. This hypothesis is tested in the framework of question-answering (QA) systems with storage requirements as a complexity measure. Shannon's rate distortion function
R(D)
represents the minimum amount of memory a system must employ in order to achieve an average distortion less than
D
(the distortion can be, for example, the average proportion of erroneous answers produced by the system). The ability of a system to convert an amount
D
of distortion into memory savings is measured by the ratio
R(D)/R(O)
. A system will be called elastic if this ratio goes to zero as the size of the dataset ensemble goes to infinity. Asymptotic bounds to
R(D)
are derived giving rise to elasticity conditions invoking the structure of the distortion matrix associated with the system. The bounds established represent a marked Improvement over former results by narrowing the gap between the necessary and sufficient conditions for elasticity. Moreover, conditions are established under which the amount of computation required for testing elasticity can be substantially reduced.