Memorias Asociativas Basadas en Relaciones de Orden y Operaciones Binarias

A new model for associative memories is proposed in this paper. The mathematical tools used in this new model, include two binary operators designed specifically for the memories developed here. These operators were arbitrarí/y named as the .first two letters from the Greek alphabet: a and fJ. The new associative memories (afJ)are oftwo kinds and are able to operate in two different modes. The operator a is useful at the learning phase, and the operator fJ is the basis for the pattern recall phase. The properties within the algebraic operators a and fJ, allow the afJ memories to exhibir simí/ar characteristics to the ones inherent to the binary version 01 the morphological associative memories, in the sense of learning capacity, type and amount 01 noise against which the memory is robust, and the s",Olcient conditions lor perfect recall. Moreover. it is important to point out that the arithmetic density 01 the proposed memories is smaller than the arithmetic density exhibited by the morphological ones. The main reason lor taking the morphological associative memories as the relerence pointfor the genesis olthe proposed ones, consist in that the authors ofthe first ones have aiready shown that the morphological associative memories are superior in some aspects to the known models of associative memories, up to.the beginning olthe third míllenium.