Energy-efficient circuit design

We initiate the theoretical investigation of energy-efficient circuit design. We assume that the circuit design speci-fies the circuit layout as well as the supply voltages for the gates. To obtain maximum energy efficiency, the circuit de-sign must balance the conflicting demands of minimizing the energy used per gate, and minimizing the number of gates in the circuit; If the energy supplied to the gates is small, then functional failures are likely, necessitating a circuit layout that is more fault-tolerant, and thus that has more gates. By leveraging previous work on fault-tolerant circuit design, we show general upper and lower bounds on the amount of energy required by a circuit to compute a given rela-tion. We show that some circuits would be asymptotically more energy-efficient if heterogeneous supply voltages were allowed, and show that for some circuits the most energy-efficient supply voltages are homogeneous over all gates