The Range of Logical Flexibility of Tree Networks

The flexible network is a network composed of flexible logical multivalued cells which 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. We have already investigated the necessary and sufficient range of flexibility of the cell's function to obtain all the output functions the network could realize. Let the network be composed of p cells and let the necesary and sufficient flexibility range of the 1th cell be denoted by φζ for ζ = 1,...,p It is shown that although the range of flexibility of the whole network φ1X ... X φpis sufficient for the network, as a whole, to produce all the output functions the network could realize, the above range is not necessary in general. Finally we derive a sufficient condition for the proposition that the range of logical flexibility of the network, φ1X ...φp, is critical. This gives a relationship between the range of logical flexibility obtained by considering a cell in the network and the one obtained by considering the whole network.