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Networks of two input-one output cells are described in which the cells are restricted to realize a subset of the 16 two-variable functions. The restriction, if appropriately chosen, will result in a network whose function set is the same as that of a network of identical structure in which each cell realizes all 16 functions. A restricted network is demonstrated which realizes exactly those functions realized by an irredundant disjunctive network which are dependent on all inputs. In addition, a restriction on cell set size is shown which produces the same functions realized by a general network in which all cells realize 16 functions. From this latter result, it can be concluded that 16 · 7c-1is an upper bound on the number of functions realizable by any network of c cells.