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Although triple modular redundancy (TMR) has been widely used to mitigate single event upsets (SEUs) in static random access memory-based field-programmable gate arrays (FPGAs), SEU-caused bridging faults between the triplicated modules do not guarantee the correctness of TMR designs under all SEUs. In this paper, we present a novel computer-aided design flow for redundancy-based applications on FPGAs in order to mitigate the impact of SEUs in the configuration bitstreams. We introduce the notions of modular redundancy conflicts and vulnerability-gap conflicts which maintain the fundamental assumption underlying the integrity of redundancy-based designs (i.e., self-containment of SEU-induced faults within a single replica of redundant resources). When the impact of SEU-induced bridging faults is considered in high-level synthesis as well as physical synthesis, on average more than 30% improvement in the number of potential SEU-induced bridging faults can be reached as well as improvements in the performance and area utilization, compared to post-synthesis TMR, in which the voters are applied to the feedback structures in the circuit. Compared to the extreme case of post-synthesis TMR in which the voters are applied at the end of every configurable logic block, we reach 38% (26%) improvement in performance(area) of the implemented circuits.