Theory of wire addition and removal in combinational Boolean networks (original) (raw)

Let w t be a wire in a combinational Boolean network. There may exist a wire w a such that when w a is added and w t is removed, the overall circuit functionality is unchanged. Redundancy-addition-and-removal (RAR) is an efficient technique to find such a w a. The idea is to add a redundant alternative wire w a to make the target wire w t redundant. However, as long as the addition of w a together with the removal of w t does not change the overall functionality of the circuit, wires that are added and removed do not necessarily need to be redundant. This raises a question about the existence of alternative wires. Why can one wire replace another wire in a combinational Boolean network? In this paper, we analyze theoretically the existence of alternative wires and model it as an error-cancellation problem. The two existing rewiring techniques, the redundancy-addition-and-removal and the global flow optimization, are unified under the proposed generalized model.