A fail-stop processor halts instead of performing an erroneous state transformation that might be visible to other processors, can detect whether another fail-stop processor has halted (due to a failure), and has a predefined portion of its storage that is unaffected by failures and accessible to any other fail-stop processor. Fail-stop processors can simplify construction of fault-tolerant computing systems. In this paper, the problem of approximating fail-stop processors is compared with the state machine approach, another general paradigm for constructing fault-tolerant systems.