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.