Bounds on memory versus error trade-offs in question-answering systems

A question-answering (QA) system answers queries from a given set about data sets drawn from a given ensemble. Shannon's rate-distortion functionR(D)provides the minimum amount of memory that a QA system must employ in order to achieve an average distortion less thanD(the distortion can, for example, be the average proportion of erroneous answers produced by the system). The ability of a system to convert an amountDof distortion into a saving in memory is measured by the ratioR(D)/R(0). A system will be called elastic if this ratio goes to zero asM, the size of the data set ensemble, tends to infinity. The asymptotic bounds toR(D)are derived, giving rise to elasticity conditions which involve only general system parameters.