Maximum projections of don't care conditions in a Boolean network

The maximum flexibility of a function at a node in a Boolean network is described by the incompletely specified function formed using the union of the satisfiability don't-care set (SDC) and observability don't-care set (ODC) of the node. The normal representation of these sets depends on every variable in the network, can be quite large and may be hard to compute. Usually, we are only interested in the don't care set when restricted to a certain set of variables. We give a formulation for the don't care set of a node in terms of a pre-specified set of variables and prove that this formulation is the maximum projection of the entire don't care set onto the chosen set of variables. This formulation allows computation to start at the target node and proceed by traversing the network outwards. The computation may be stopped at any time yielding a valid subset of the don't care set.