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Near-threshold operation can increase the number of simultaneously active cores at the expense of much lower operating frequency ("dim silicon"), but dim cores suffer from diminishing returns as the number of cores increases. At this point, hardware accelerators become more efficient alternatives. To explore such a broad design space, the authors present an analytical model to quantify the performance limits of many-core, heterogeneous systems operating at near-threshold voltage. The model augments Amdahl's law with detailed scaling of frequency and power, calibrated by circuit-level simulations using a modified Predictive Technology Model (PTM), and factors in the effects of process variations. Results show that dim cores do indeed boost throughput, even in the presence of process variations, but significant benefits are achieved only in applications with high parallelism or novel architectures to mitigate variation. Reconfigurable logic that supports a variety of accelerators is more beneficial than "dim cores" or dedicated, fixed-logic accelerators, unless the kernel targeted by fixed logic has overwhelming coverage across applications, or the speedup of the dedicated accelerator over the reconfigurable equivalent is significant.