Logical Networks of Flexible Cells

The flexible network is a network composed of flexible logical multivalued cells that can be adjusted at will to perform any functions. The network is assumed to have a fixed-interconnection pattern and to have a fixed-input variable assignment. The following question is answered. What is the necessary and sufficient range of the flexibility of the cells' functions to obtain all the output functions the circuit could realize? Furthermore, the relation between the cells functions that realize the same output functions is derived and the number of different realizable output functions is counted.