Fixed points of autoassociative morphological memories

We recently introduced a class of highly nonlinear associative memories called morphological associative memories. We have previously shown that autoassociative morphological memories (AMMs) exhibit many desirable characteristics, including optimal absolute storage capacity and one-step convergence (G.X. Ritter et al., 1998). Other aspects of AMM performance still require more detailed analysis and/or improvement. The paper provides considerable insight into the functionality of AMMs by giving necessary and sufficient conditions for fixed points. We then show that the output generated upon presentation of an input pattern x is either the smallest fixed point ⩾x or the largest fixed point ⩽x