We initiate the theoretical investigation of energy-efficient circuit design. We assume that the circuit design specifies the circuit layout as well as the supply voltages for the gates. To obtain maximum energy efficiency, the circuit design 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 relation. 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. Additionally, we show hardness and approximation results for the problem of finding the minimum energy required by a fixed circuit to compute a relation.

Joint work with Antonios Antoniadis, Neal Barcelo, Kirk Pruhs, and Michele Scquizzato

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