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We propose an approach for reducing the TSO reachability analysis of concurrent programs to their SC reachability analysis, under some conditions on the explored behaviors. First, we propose a linear code-to-code translation that takes as input a concurrent program P and produces a concurrent program P′ such that, running P′ under SC yields the same set of reachable (shared) states as running P under TSO with at most k context-switches for each thread, for a fixed k. Basically, we show that it is possible to use only O(k) additional copies of the shared variables of P as local variables to simulate the store buffers, even if they are unbounded. Furthermore, we show that our translation can be extended so that an unbounded number of context-switches is possible, under the condition that each write operation sent to the store buffer stays there for at most k context-switches of the thread. Experimental results show that bugs due to TSO can be detected with small bounds, using off-the-shelf SC analysis tools.