We present instance-specific custom computing machines for the set covering problem. Four accelerator architectures are developed that implement branch & bound in 3-valued logic and many of the deduction techniques found in software solvers. We use set covering benchmarks from two-level logic minimization and Steiner triple systems to derive and discuss experimental results. The resulting raw speedups are in the order of four magnitudes on average. Finally, we propose a hybrid solver architecture that combines the raw speed of instance-specific reconfigurable hardware with flexible bounding schemes implemented in software.