Complexity-theoretic obstacles to achieving energy savings with near-threshold computing

In the traditional approach to circuit design the supply voltages for each transistor/gate are set sufficiently high so that with sufficiently high probability no transistor fails. One potential method to attain more energy-efficient circuits is Near-Threshold Computing, which simply means that the supply voltages are designed to be closer to the threshold voltage. However, this energy saving comes at a cost of a greater probability of functional failure, which necessitates that the circuits must be more fault tolerant, and thus contain more gates. Thus achieving energy savings with Near-Threshold Computing involves properly balancing the energy used per gate with the number of gates used. We show that if there is a better (in terms of worst-case relative error with respect to energy) method than the traditional approach then P = NP, and thus there is a complexity theoretic obstacle to achieving energy savings with Near-Threshold Computing.