The neuro-network equivalent models of multiport optical associative memory (MOAM) with different training rules are considered. The given models use image weighting in order to increase memory capacity while storing highly correlated images. The algorithms of the model's implementation are also suggested. The mathematical background of all these models are basic operations equivalence of continual logic and Boolean operations of coincidence, vector-matrix, and matrix-matrix procedures with those basic operations. The generality and acceptability of equivalent models application for the description of MOAM and neuro-networks (NN) with different coding methods and image representation are shown. All this creates the possibilities for the creation of digital as well as analogue memory. The results of modeling exemplified by the storage and recognition of all the letters of English alphabet are considered. Means of MOAM and NN based on these models implementation are suggested and discussed. The performance of the models is 10$+10$/ divided by 10$+11$/ connections/sec, they do not require the storage of matrix interconnections multilevel weights. These weights are formed in the course of calculations while recalculating networks, and the pattern images but not weights are stored in a single memory. Basic devices for MOAM and NN implementation on the base of equivalence models are matrix-matrix equivalators (MME).
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