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We analyze two algorithms for the k-exclusion problem on the asynchronous multi-writer/reader shared memory model and show their correctness. The first algorithm is a natural extension of the n-process algorithm by Peterson for the mutual exclusion algorithm to the k-exclusion problem, and the second algorithm is a combination of the first algorithm and the tournament algorithm by Peterson and Fischer for the mutual exclusion problem. These two algorithms satisfy k-exclusion, and can tolerate up to k À 1 process failures of the stopping type. The running times by the first algorithm and by the second algorithm are bounded by ðn À kÞc þ Oðnðn À kÞ 2 Þl and ð n k Þ k c þ Oðð n k Þ kþ1 kÞl, respectively, even if there exist at most k À 1 process failures of the stopping type, where n is the number of processes, l is an upper bound on the time between successive two atomic steps for any faultless process, and c is an upper bound on the time that any user spends in the critical region.

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