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SRAM-based FPGAs are susceptible to Single-Event Upsets (SEUs) in radiation-exposed environments due to their configuration memory. We propose a new scheme for the diagnosis and recovery from upsets that combines i) duplication of the core to be protected, ii) partial reconfiguration to reconfigure the faulty part only, and iii) hardcore processor(s) for deciding when and which part will be reconfigured; executing the application in software instead of hardware during fault handling; and controlling the reconfiguration. A hardcore processor has smaller cross section and it is less susceptible than reconfigurable resources. Thus it can temporarily undertake the execution during upset conditions. Real experiments demonstrate that our approach is feasible and an area reduction of more than 40% over the dominant Triple Modular Redundancy (TMR) solution can be achieved at the cost of a reduction in the processing rate of the input.