Almost every wire is removable: a modeling and solution for removing any circuit wire

Rewiring is a flexible and useful logic transformation technique through which a target wire can be removed by adding its alternative logics without changing the circuit functionality. In today's deep sub-micron era, circuit wires have become a dominating factor in most EDA processes and there are situations where removing a certain set of (perhaps extremely unwanted) wires is very useful. However, it has been experimentally suggested that the rewiring rate (percentage of original circuit wires being removable by rewiring) is only 30 to 40% for optimized circuits in the past. In this paper, we propose a generalized error cancellation modeling and flow to show that theoretically almost every circuit wire is removable under this flow. In the Flow graph Error Cancellation based Rewiring (FECR) scheme we propose here, a rewiring rate of 95% of even optimized circuits is obtainable under this scheme, affirming the basic claim of this paper. To our knowledge, this is the first known rewiring scheme being able to achieve this near complete rewiring rate. Consequently, this wire-removal process can now be considered as a powerful atomic and universal operation for logic transformations, as virtually every circuit node can also be removed through repetitions of this rewiring process. Besides, this modeling can also serve as a general framework containing many other rewiring techniques as its special cases.