The κ-set consensus problem requires processes to decide on at most κ of their input values. The problem can be solved using only read / write operations in the presence of f crash failures if and only if f < κ. One way to subvert this impossibility result is to restrict the set of possible assignments of input values to processes. This paper presents a characterization of the input restrictions that allow a wait-free solution of n-set consensus in a system with n + 1 processes, using only read and write operations.
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