On the characteristics of the quadratic order associative memory that uses synchronous update and direct convergence

A statistical method is applied to explore the characteristics of a certain class of quadratic order associative memories: the Synchronous Update Direct Convergence Memory (SQDM). The initial input vector is required to converge, with a given value of probability Pdc, to a stored codeword in just one synchronous update. The memory capacity ms is derived by a figure of merit N phi, and its tight asymptotic bound is found by using Tchebycheff's inequality. When the input contains erroneous bits, the maximum allowable number of attractors and their attraction radii are determined. The existence of principal connections Tpr useful in solving the problem of proliferation of connections in the SQDM is introduced. We proved that Tpr is a set of which an arbitrary connection Tijk satisfies square root of ms < or = [Tijk[ < or = 2 square root of ms.