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The current paper contains the theoretical foundation for the off-the-mainstream model known as Alpha-Beta associative memories (αβαβ model). This is an unconventional computation model designed to operate as an associative memory, whose main application is the solution of pattern recognition tasks, particularly for pattern recall and pattern classification. Although this model was devised, proposed and created in 2002, it is worth noting that its theoretical support remains unpublished to this day. This is despite the fact that more than a hundred scientific articles have been published with applications, improvements, and new models derived from the αβ model. The present paper includes all the required definitions, and the rigorous mathematical demonstrations of the lemmas and theorems, explaining the operation of the αβ model, as well as the original models it has inspired or that have been derived from it. Also, brief descriptions of 60 selected articles related to the αβ model are presented. These latter works illustrate the competitiveness (and sometimes superiority) of several extensions and models derived from the original αβ model, when compared against some models and paradigms present in the mainstream current scientific literature.
Associative memory, Binary operation, Order relation, αβ associative memories