A method of network synthesis for general combinational functions that uses a number of fixed threshold logic units not greatly in excess of the theoretical minimum is described. It can be used with adaptive logic in which case a minority of the interconnections are simply adapted once according to the rule originally suggested by Hebb. This network on its own has no capacity for generalization,'' and if used for pattern recognition must therefore be operated in conjunction with a suitable property filter, such as that of the previous paper.[<sup>1</sup>] In this case the present network could perform as a trainable categorizer.''