LINEAR SEPARABILITY OF POSITIVE SELF-DUAL LOGICAL FILTERS

The threshold logic filter is an important nonlinear filter class, whi ch is defined by a threshold logic function of binary input values. It is proved in this paper that not all positive self-dual logical funct ions are threshold functions if the number of input variables is 5 or more. The positive self-dual logical filter is a limited class but inc ludes almost all filters for noise removal. Our result means that not all positive self-dual filters can be expressed by one operation of th e threshold logic filters. In the sense of the filter expression by ne ural networks, the two-layer network cannot always optimize even this limited class.