Observability relations and observability don´t cares

The observability relation O(x,z) or the Boolean relation provides a description of all the flexibility one has in implementing a Boolean network N. The authors represent and use this flexibility in a logic synthesis system by adding a single output node to the Boolean network N. The node function for the new node is O(x,z). The newly constructed network N´ (called the observability network) has only one output and computes 1 for every input x. It is shown that the observability don´t cares (ODCs) for a node y/sub i/ in N´ provide the maximum flexibility for implementing y/sub i/ and subsume the flexibility obtained for y/sub i/ in N even with don´t cares provided at each output. This gives rise to new methods for computing complete ODCs for N´ and hence for N.<>