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Mapping programs from one architecture to another plays a key role in technologies such as binary translation, decompilation, emulation, virtualization, and application migration. Although multicore architectures are ubiquitous, the state-of-the-art translation tools do not handle concurrency primitives correctly. Doing so is rather challenging because of the subtle differences in the concurrency models between architectures. In response, we address various aspects of the challenge. First, we develop correct and efficient translations between the concurrency models of two mainstream architecture families: x86 and ARM (versions 7 and 8). We develop direct mappings between x86 and ARMv8 and ARMv7, and fence elimination algorithms to eliminate redundant fences after direct mapping. Although our mapping utilizes ARMv8 as an intermediate model for mapping between x86 and ARMv7, we argue that it should not be used as an intermediate model in a decompiler because it disallows common compiler transformations. Second, we propose and implement a technique for inserting memory fences for safely migrating programs between different architectures. Our technique checks robustness against x86 and ARM, and inserts fences upon robustness violations. Our experiments demonstrate that in most of the programs both our techniques introduce significantly fewer fences compared to naive schemes for porting applications across these architectures.